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Ressler.\n-This manual is for sketch, version 0.3 (build 7), Friday, June 20, 2025, a program that\n+This manual is for sketch, version 0.3 (build 7), Sunday, May 19, 2024, a program that\n converts descriptions of simple three-dimensional scenes into line drawings. This version\n generates PSTricks or PGF/TikZ code suitable for use with the TEX document processing\n system.\n Sketch is free software. You can redistribute it and/or modify it under the terms of the\n GNU General Public License as published by the Free Software Foundation; either version\n 3, or (at your option) any later version.\n Sketch is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;\n"}]}]}, {"source1": "./usr/share/info/sketch.info.gz", "source2": "./usr/share/info/sketch.info.gz", "unified_diff": null, "details": [{"source1": "sketch.info", "source2": "sketch.info", "has_internal_linenos": true, "unified_diff": "@@ -5,9793 +5,9793 @@\n 00000040: 682e 7465 7869 2e0a 0a43 6f70 7972 6967 h.texi...Copyrig\n 00000050: 6874 20c2 a920 3230 3035 2074 6f20 3230 ht .. 2005 to 20\n 00000060: 3132 2045 7567 656e 6520 4b2e 2052 6573 12 Eugene K. Res\n 00000070: 736c 6572 2e0a 0a20 2020 5468 6973 206d sler... 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You\n+00000660: 2063 616e 2072 6564 6973 7472 6962 7574 can redistribut\n+00000670: 6520 6974 2061 6e64 2f6f 7220 6d6f 6469 e it and/or modi\n+00000680: 6679 2069 740a 756e 6465 7220 7468 6520 fy it.under the \n+00000690: 7465 726d 7320 6f66 2074 6865 2047 4e55 terms of the GNU\n+000006a0: 2047 656e 6572 616c 2050 7562 6c69 6320 General Public \n+000006b0: 4c69 6365 6e73 6520 6173 2070 7562 6c69 License as publi\n+000006c0: 7368 6564 2062 7920 7468 650a 4672 6565 shed by the.Free\n+000006d0: 2053 6f66 7477 6172 6520 466f 756e 6461 Software Founda\n+000006e0: 7469 6f6e 3b20 6569 7468 6572 2076 6572 tion; either ver\n+000006f0: 7369 6f6e 2033 2c20 6f72 2028 6174 2079 sion 3, or (at y\n+00000700: 6f75 7220 6f70 7469 6f6e 2920 616e 790a our option) any.\n+00000710: 6c61 7465 7220 7665 7273 696f 6e2e 0a0a later version...\n+00000720: 2020 2053 6b65 7463 6820 6973 2064 6973 Sketch is dis\n+00000730: 7472 6962 7574 6564 2069 6e20 7468 6520 tributed in the \n+00000740: 686f 7065 2074 6861 7420 6974 2077 696c hope that it wil\n+00000750: 6c20 6265 2075 7365 6675 6c2c 2062 7574 l be useful, but\n+00000760: 2057 4954 484f 5554 0a41 4e59 2057 4152 WITHOUT.ANY WAR\n+00000770: 5241 4e54 593b 2077 6974 686f 7574 2065 RANTY; without e\n+00000780: 7665 6e20 7468 6520 696d 706c 6965 6420 ven the implied \n+00000790: 7761 7272 616e 7479 206f 6620 4d45 5243 warranty of MERC\n+000007a0: 4841 4e54 4142 494c 4954 5920 6f72 0a46 HANTABILITY or.F\n+000007b0: 4954 4e45 5353 2046 4f52 2041 2050 4152 ITNESS FOR A PAR\n+000007c0: 5449 4355 4c41 5220 5055 5250 4f53 452e TICULAR PURPOSE.\n+000007d0: 2053 6565 2074 6865 2047 4e55 2047 656e See the GNU Gen\n+000007e0: 6572 616c 2050 7562 6c69 6320 4c69 6365 eral Public Lice\n+000007f0: 6e73 6520 666f 720a 6d6f 7265 2064 6574 nse for.more det\n+00000800: 6169 6c73 2e0a 0a20 2020 596f 7520 7368 ails... You sh\n+00000810: 6f75 6c64 2068 6176 6520 7265 6365 6976 ould have receiv\n+00000820: 6564 2061 2063 6f70 7920 6f66 2074 6865 ed a copy of the\n+00000830: 2047 4e55 2047 656e 6572 616c 2050 7562 GNU General Pub\n+00000840: 6c69 6320 4c69 6365 6e73 650a 616c 6f6e lic License.alon\n+00000850: 6720 7769 7468 20e2 8098 736b 6574 6368 g with ...sketch\n+00000860: e280 993b 2073 6565 2074 6865 2066 696c ...; see the fil\n+00000870: 6520 434f 5059 494e 472e 7478 742e 2020 e COPYING.txt. \n+00000880: 4966 206e 6f74 2c20 7365 650a 6874 7470 If not, see.http\n+00000890: 3a2f 2f77 7777 2e67 6e75 2e6f 7267 2f63 ://www.gnu.org/c\n+000008a0: 6f70 796c 6566 742e 0a0a 2a20 4d65 6e75 opyleft...* Menu\n+000008b0: 3a0a 0a2a 2041 626f 7574 2073 6b65 7463 :..* About sketc\n+000008c0: 683a 3a20 2020 2020 2020 2020 2020 2020 h:: \n+000008d0: 2020 2057 6879 2073 6b65 7463 6820 6578 Why sketch ex\n+000008e0: 6973 7473 2061 6e64 2077 6861 7420 6974 ists and what it\n+000008f0: 2064 6f65 732e 0a2a 2049 6e74 726f 6475 does..* Introdu\n+00000900: 6374 696f 6e20 6279 2065 7861 6d70 6c65 ction by example\n+00000910: 3a3a 2020 2020 204d 6f73 7420 6665 6174 :: Most feat\n+00000920: 7572 6573 2073 686f 776e 2061 7320 776f ures shown as wo\n+00000930: 726b 696e 6720 636f 6465 2e0a 2a20 496e rking code..* In\n+00000940: 7075 7420 6c61 6e67 7561 6765 3a3a 2020 put language:: \n+00000950: 2020 2020 2020 2020 2020 2020 5379 6e74 Synt\n+00000960: 6178 2061 6e64 2073 656d 616e 7469 6373 ax and semantics\n+00000970: 206f 6620 e280 9873 6b65 7463 68e2 8099 of ...sketch...\n+00000980: 2063 6f6d 6d61 6e64 732e 0a2a 2042 7569 commands..* Bui\n+00000990: 6c64 696e 6720 6120 6472 6177 696e 673a lding a drawing:\n+000009a0: 3a20 2020 2020 2020 2020 2048 6f77 2074 : How t\n+000009b0: 6f20 7573 6520 e280 9873 6b65 7463 68e2 o use ...sketch.\n+000009c0: 8099 2070 726f 6475 6374 6976 656c 792e .. productively.\n+000009d0: 0a2a 2043 6f6d 6d61 6e64 206c 696e 653a .* Command line:\n+000009e0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+000009f0: 204f 7074 696f 6e73 2061 6e64 2074 6865 Options and the\n+00000a00: 6972 2075 7361 6765 2e0a 2a20 496e 7374 ir usage..* Inst\n+00000a10: 616c 6c69 6e67 2073 6b65 7463 683a 3a20 alling sketch:: \n+00000a20: 2020 2020 2020 2020 2020 4275 696c 6469 Buildi\n+00000a30: 6e67 2061 6e64 2069 6e73 7461 6c6c 696e ng and installin\n+00000a40: 6720 6672 6f6d 2073 6f75 7263 6573 2e0a g from sources..\n+00000a50: 2a20 496e 6465 7820 6f66 2073 796e 7461 * Index of synta\n+00000a60: 783a 3a0a 2a20 496e 6465 783a 3a0a 0a20 x::.* Index::.. \n+00000a70: 2d2d 2054 6865 2044 6574 6169 6c65 6420 -- The Detailed \n+00000a80: 4e6f 6465 204c 6973 7469 6e67 202d 2d0a Node Listing --.\n+00000a90: 0a41 626f 7574 2073 6b65 7463 680a 0a2a .About sketch..*\n+00000aa0: 2052 6570 6f72 7469 6e67 2062 7567 733a Reporting bugs:\n+00000ab0: 3a20 2020 2020 2020 2020 2020 2020 204c : L\n+00000ac0: 6574 2075 7365 206b 6e6f 7720 7768 6174 et use know what\n+00000ad0: 2773 2077 726f 6e67 210a 2a20 436f 6e74 's wrong!.* Cont\n+00000ae0: 7269 6275 7469 6f6e 733a 3a20 2020 2020 ributions:: \n+00000af0: 2020 2020 2020 2020 2020 486f 7720 796f How yo\n+00000b00: 7520 6361 6e20 6865 6c70 2e2e 2e2e 0a0a u can help......\n+00000b10: 496e 7472 6f64 7563 7469 6f6e 2062 7920 Introduction by \n+00000b20: 6578 616d 706c 650a 0a2a 2048 656c 6c6f example..* Hello\n+00000b30: 2077 6f72 6c64 3a3a 2020 2020 2020 2020 world:: \n+00000b40: 2020 2020 2020 2020 2053 696d 706c 6573 Simples\n+00000b50: 7420 706f 7373 6962 6c65 20e2 8098 736b t possible ...sk\n+00000b60: 6574 6368 e280 9920 7072 6f67 7261 6d2e etch... program.\n+00000b70: 0a2a 2044 7261 7769 6e67 206f 7074 696f .* Drawing optio\n+00000b80: 6e73 3a3a 2020 2020 2020 2020 2020 2020 ns:: \n+00000b90: 2043 6f6e 7472 6f6c 6c69 6e67 206f 626a Controlling obj\n+00000ba0: 6563 7420 6170 7065 6172 616e 6365 2e0a ect appearance..\n+00000bb0: 2a20 4472 6177 696e 6720 6120 736f 6c69 * Drawing a soli\n+00000bc0: 643a 3a20 2020 2020 2020 2020 2020 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2020 2020 2020 2020 2020 4472 6177 2064 Draw d\n+00001460: 6f74 732e 0a2a 204c 696e 6573 3a3a 2020 ots..* Lines:: \n 00001470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001480: 2020 2020 2020 2044 7261 7720 706f 6c79 Draw poly\n-00001490: 6c69 6e65 732e 0a2a 2043 7572 7665 733a lines..* Curves:\n-000014a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000014b0: 2020 2020 2020 2044 7261 7720 6375 7276 Draw curv\n-000014c0: 6573 2e0a 2a20 506f 6c79 676f 6e73 3a3a es..* Polygons::\n+00001480: 2020 2020 2044 7261 7720 706f 6c79 6c69 Draw polyli\n+00001490: 6e65 732e 0a2a 2043 7572 7665 733a 3a20 nes..* Curves:: \n+000014a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000014b0: 2020 2020 2044 7261 7720 6375 7276 6573 Draw curves\n+000014c0: 2e0a 2a20 506f 6c79 676f 6e73 3a3a 2020 ..* Polygons:: \n 000014d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000014e0: 2020 2020 4472 6177 2070 6f6c 7967 6f6e Draw polygon\n-000014f0: 732e 0a2a 2053 7065 6369 616c 733a 3a20 s..* Specials:: 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6d65 Draw transforme\n-000015e0: 6420 636f 7069 6573 206f 6620 6f62 6a65 d copies of obje\n-000015f0: 6374 732e 0a2a 2050 7574 733a 3a20 2020 cts..* Puts:: \n+00001510: 2045 6d62 6564 2072 6177 204c 6154 6558 Embed raw LaTeX\n+00001520: 2061 6e64 20e2 8098 5053 5472 6963 6b73 and ...PSTricks\n+00001530: e280 992e 0a2a 2053 7765 6570 733a 3a20 .....* Sweeps:: \n+00001540: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00001550: 2020 2020 2044 7261 7720 7377 6565 7073 Draw sweeps\n+00001560: 206f 6620 646f 7473 2061 6e64 2070 6f6c of dots and pol\n+00001570: 796c 696e 6573 2e0a 2a20 426c 6f63 6b73 ylines..* Blocks\n+00001580: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+00001590: 2020 2020 2020 2020 4772 6f75 7020 6f74 Group ot\n+000015a0: 6865 7220 6472 6177 6162 6c65 732e 0a2a her drawables..*\n+000015b0: 2052 6570 6561 7473 3a3a 2020 2020 2020 Repeats:: \n+000015c0: 2020 2020 2020 2020 2020 2020 2020 2044 D\n+000015d0: 7261 7720 7472 616e 7366 6f72 6d65 6420 raw transformed \n+000015e0: 636f 7069 6573 206f 6620 6f62 6a65 6374 copies of object\n+000015f0: 732e 0a2a 2050 7574 733a 3a20 2020 2020 s..* Puts:: \n 00001600: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001610: 2020 2020 2044 7261 7720 6f6e 6520 6f62 Draw one ob\n-00001620: 6a65 6374 2074 7261 6e73 666f 726d 6564 ject transformed\n-00001630: 2e0a 0a53 7765 6570 730a 0a2a 2053 7765 ...Sweeps..* Swe\n-00001640: 7074 2070 6f69 6e74 733a 3a20 2020 2020 pt points:: \n-00001650: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n-00001660: 2070 6f69 6e74 7320 6d61 6b65 206c 696e points make lin\n-00001670: 6573 206f 7220 706f 6c79 676f 6e73 2e0a es or polygons..\n-00001680: 2a20 5377 6570 7420 6c69 6e65 733a 3a20 * Swept lines:: \n-00001690: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000016a0: 5377 6570 7420 6c69 6e65 7320 6d61 6b65 Swept lines make\n-000016b0: 206f 7065 6e20 6f72 2063 6c6f 7365 6420 open or closed \n-000016c0: 7375 7266 6163 6573 2e0a 2a20 5377 6570 surfaces..* Swep\n-000016d0: 7420 706f 6c79 676f 6e73 3a3a 2020 2020 t polygons:: \n-000016e0: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n-000016f0: 706f 6c79 676f 6e73 206d 616b 6520 636c polygons make cl\n-00001700: 6f73 6564 2073 7572 6661 6365 732e 0a2a osed surfaces..*\n-00001710: 2053 7765 7074 2062 6c6f 636b 733a 3a20 Swept blocks:: \n-00001720: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-00001730: 7765 7074 2062 6c6f 636b 20e2 89a1 2062 wept block ... b\n-00001740: 6c6f 636b 206f 6620 7377 6565 7073 2e0a lock of sweeps..\n-00001750: 2a20 5377 6565 7020 6661 6365 2073 706c * Sweep face spl\n-00001760: 6974 7469 6e67 3a3a 2020 2020 2020 2020 itting:: \n-00001770: 4669 7869 6e67 2077 6172 7065 6420 6661 Fixing warped fa\n-00001780: 6365 7320 7769 7468 2074 7269 616e 676c ces with triangl\n-00001790: 6573 2e0a 0a44 6566 696e 6974 696f 6e73 es...Definitions\n-000017a0: 0a0a 2a20 466f 726d 7320 6f66 2064 6566 ..* Forms of def\n-000017b0: 696e 6974 696f 6e73 3a3a 2020 2020 2020 initions:: \n-000017c0: 2020 4469 6666 6572 656e 7420 6465 6673 Different defs\n-000017d0: 2066 6f72 2064 6966 6665 7265 6e74 2070 for different p\n-000017e0: 7572 706f 7365 732e 0a2a 2046 6f72 6d73 urposes..* Forms\n-000017f0: 206f 6620 7265 6665 7265 6e63 6573 3a3a of references::\n-00001800: 2020 2020 2020 2020 2048 6f77 2072 6566 How ref\n-00001810: 6572 656e 6365 7320 6465 6e6f 7465 2074 erences denote t\n-00001820: 7970 6573 2e0a 0a47 6c6f 6261 6c20 656e ypes...Global en\n-00001830: 7669 726f 6e6d 656e 740a 0a2a 2047 6c6f vironment..* Glo\n-00001840: 6261 6c20 6f70 7469 6f6e 733a 3a20 2020 bal options:: \n-00001850: 2020 2020 2020 2020 2020 2041 7474 7269 Attri\n-00001860: 6275 7465 7320 6f66 2074 6865 2065 6e74 butes of the ent\n-00001870: 6972 6520 6472 6177 696e 672e 0a2a 2043 ire drawing..* C\n-00001880: 616d 6572 613a 3a20 2020 2020 2020 2020 amera:: \n-00001890: 2020 2020 2020 2020 2020 2020 2041 2066 A f\n-000018a0: 696e 616c 2063 616d 6572 6120 7472 616e inal camera tran\n-000018b0: 7366 6f72 6d61 7469 6f6e 206f 6620 7468 sformation of th\n-000018c0: 6520 7363 656e 652e 0a2a 2050 6963 7475 e scene..* Pictu\n-000018d0: 7265 2062 6f78 3a3a 2020 2020 2020 2020 re box:: \n-000018e0: 2020 2020 2020 2020 2053 6574 7469 6e67 Setting\n-000018f0: 2074 6865 2062 6f75 6e64 696e 6720 626f the bounding bo\n-00001900: 7820 616e 6420 3264 2063 6c69 7070 696e x and 2d clippin\n-00001910: 672e 0a2a 2046 7261 6d65 3a3a 2020 2020 g..* Frame:: \n+00001610: 2020 2044 7261 7720 6f6e 6520 6f62 6a65 Draw one obje\n+00001620: 6374 2074 7261 6e73 666f 726d 6564 2e0a ct transformed..\n+00001630: 0a53 7765 6570 730a 0a2a 2053 7765 7074 .Sweeps..* Swept\n+00001640: 2070 6f69 6e74 733a 3a20 2020 2020 2020 points:: \n+00001650: 2020 2020 2020 2020 2053 7765 7074 2070 Swept p\n+00001660: 6f69 6e74 7320 6d61 6b65 206c 696e 6573 oints make lines\n+00001670: 206f 7220 706f 6c79 676f 6e73 2e0a 2a20 or polygons..* \n+00001680: 5377 6570 7420 6c69 6e65 733a 3a20 2020 Swept lines:: \n+00001690: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+000016a0: 6570 7420 6c69 6e65 7320 6d61 6b65 206f ept lines make o\n+000016b0: 7065 6e20 6f72 2063 6c6f 7365 6420 7375 pen or closed su\n+000016c0: 7266 6163 6573 2e0a 2a20 5377 6570 7420 rfaces..* Swept \n+000016d0: 706f 6c79 676f 6e73 3a3a 2020 2020 2020 polygons:: \n+000016e0: 2020 2020 2020 2020 5377 6570 7420 706f Swept po\n+000016f0: 6c79 676f 6e73 206d 616b 6520 636c 6f73 lygons make clos\n+00001700: 6564 2073 7572 6661 6365 732e 0a2a 2053 ed surfaces..* S\n+00001710: 7765 7074 2062 6c6f 636b 733a 3a20 2020 wept blocks:: \n+00001720: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00001730: 7074 2062 6c6f 636b 20e2 89a1 2062 6c6f pt block ... blo\n+00001740: 636b 206f 6620 7377 6565 7073 2e0a 2a20 ck of sweeps..* \n+00001750: 5377 6565 7020 6661 6365 2073 706c 6974 Sweep face split\n+00001760: 7469 6e67 3a3a 2020 2020 2020 2020 4669 ting:: Fi\n+00001770: 7869 6e67 2077 6172 7065 6420 6661 6365 xing warped face\n+00001780: 7320 7769 7468 2074 7269 616e 676c 6573 s with triangles\n+00001790: 2e0a 0a44 6566 696e 6974 696f 6e73 0a0a ...Definitions..\n+000017a0: 2a20 466f 726d 7320 6f66 2064 6566 696e * Forms of defin\n+000017b0: 6974 696f 6e73 3a3a 2020 2020 2020 2020 itions:: \n+000017c0: 4469 6666 6572 656e 7420 6465 6673 2066 Different defs f\n+000017d0: 6f72 2064 6966 6665 7265 6e74 2070 7572 or different pur\n+000017e0: 706f 7365 732e 0a2a 2046 6f72 6d73 206f poses..* Forms o\n+000017f0: 6620 7265 6665 7265 6e63 6573 3a3a 2020 f references:: \n+00001800: 2020 2020 2020 2048 6f77 2072 6566 6572 How refer\n+00001810: 656e 6365 7320 6465 6e6f 7465 2074 7970 ences denote typ\n+00001820: 6573 2e0a 0a47 6c6f 6261 6c20 656e 7669 es...Global envi\n+00001830: 726f 6e6d 656e 740a 0a2a 2047 6c6f 6261 ronment..* Globa\n+00001840: 6c20 6f70 7469 6f6e 733a 3a20 2020 2020 l options:: \n+00001850: 2020 2020 2020 2020 2041 7474 7269 6275 Attribu\n+00001860: 7465 7320 6f66 2074 6865 2065 6e74 6972 tes of the entir\n+00001870: 6520 6472 6177 696e 672e 0a2a 2043 616d e drawing..* Cam\n+00001880: 6572 613a 3a20 2020 2020 2020 2020 2020 era:: \n+00001890: 2020 2020 2020 2020 2020 2041 2066 696e A fin\n+000018a0: 616c 2063 616d 6572 6120 7472 616e 7366 al camera transf\n+000018b0: 6f72 6d61 7469 6f6e 206f 6620 7468 6520 ormation of the \n+000018c0: 7363 656e 652e 0a2a 2050 6963 7475 7265 scene..* Picture\n+000018d0: 2062 6f78 3a3a 2020 2020 2020 2020 2020 box:: \n+000018e0: 2020 2020 2020 2053 6574 7469 6e67 2074 Setting t\n+000018f0: 6865 2062 6f75 6e64 696e 6720 626f 7820 he bounding box \n+00001900: 616e 6420 3264 2063 6c69 7070 696e 672e and 2d clipping.\n+00001910: 0a2a 2046 7261 6d65 3a3a 2020 2020 2020 .* Frame:: \n 00001920: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001930: 2020 2041 6464 696e 6720 6120 626f 7820 Adding a box \n-00001940: 6172 6f75 6e64 2074 6865 2064 7261 7769 around the drawi\n-00001950: 6e67 2e0a 2a20 4c61 6e67 7561 6765 3a3a ng..* Language::\n+00001930: 2041 6464 696e 6720 6120 626f 7820 6172 Adding a box ar\n+00001940: 6f75 6e64 2074 6865 2064 7261 7769 6e67 ound the drawing\n+00001950: 2e0a 2a20 4c61 6e67 7561 6765 3a3a 2020 ..* Language:: \n 00001960: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001970: 2020 2020 5365 7474 696e 6720 7468 6520 Setting the \n-00001980: 6f75 7470 7574 206c 616e 6775 6167 652e output language.\n-00001990: 0a0a 4275 696c 6469 6e67 2061 2064 7261 ..Building a dra\n-000019a0: 7769 6e67 0a0a 2a20 4f76 6572 7669 6577 wing..* Overview\n-000019b0: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n-000019c0: 2020 2020 2020 4275 696c 6469 6e67 2061 Building a\n-000019d0: 2073 7562 7374 616e 7469 616c 2064 7261 substantial dra\n-000019e0: 7769 6e67 2e0a 2a20 4120 7465 6368 6e69 wing..* A techni\n-000019f0: 6361 6c20 6472 6177 696e 673a 3a20 2020 cal drawing:: \n-00001a00: 2020 2020 2020 416e 2065 7861 6d70 6c65 An example\n-00001a10: 2077 6974 6820 6669 6e65 2070 6c61 6365 with fine place\n-00001a20: 6d65 6e74 2e0a 2a20 4120 6869 6572 6172 ment..* A hierar\n-00001a30: 6368 6963 616c 206d 6f64 656c 3a3a 2020 chical model:: \n-00001a40: 2020 2020 2020 416e 2065 7861 6d70 6c65 An example\n-00001a50: 2077 6974 6820 7377 6565 7073 2061 6e64 with sweeps and\n-00001a60: 2070 7574 732e 0a2a 2043 6176 6561 7473 puts..* Caveats\n-00001a70: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n-00001a80: 2020 2020 2020 2057 6865 7265 2074 726f Where tro\n-00001a90: 7562 6c65 2063 616e 206f 6363 7572 2e0a uble can occur..\n-00001aa0: 0a43 6176 6561 7473 0a0a 2a20 4c69 6d69 .Caveats..* Limi\n-00001ab0: 7473 206f 6e20 6572 726f 7220 6465 7465 ts on error dete\n-00001ac0: 6374 696f 6e3a 3a20 2020 5768 6174 2073 ction:: What s\n-00001ad0: 6b65 7463 6820 646f 6573 6e27 7420 646f ketch doesn't do\n-00001ae0: 2e0a 2a20 436c 6970 7069 6e67 3a3a 2020 ..* Clipping:: \n+00001970: 2020 5365 7474 696e 6720 7468 6520 6f75 Setting the ou\n+00001980: 7470 7574 206c 616e 6775 6167 652e 0a0a tput language...\n+00001990: 4275 696c 6469 6e67 2061 2064 7261 7769 Building a drawi\n+000019a0: 6e67 0a0a 2a20 4f76 6572 7669 6577 3a3a ng..* Overview::\n+000019b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000019c0: 2020 2020 4275 696c 6469 6e67 2061 2073 Building a s\n+000019d0: 7562 7374 616e 7469 616c 2064 7261 7769 ubstantial drawi\n+000019e0: 6e67 2e0a 2a20 4120 7465 6368 6e69 6361 ng..* A technica\n+000019f0: 6c20 6472 6177 696e 673a 3a20 2020 2020 l drawing:: \n+00001a00: 2020 2020 416e 2065 7861 6d70 6c65 2077 An example w\n+00001a10: 6974 6820 6669 6e65 2070 6c61 6365 6d65 ith fine placeme\n+00001a20: 6e74 2e0a 2a20 4120 6869 6572 6172 6368 nt..* A hierarch\n+00001a30: 6963 616c 206d 6f64 656c 3a3a 2020 2020 ical model:: \n+00001a40: 2020 2020 416e 2065 7861 6d70 6c65 2077 An example w\n+00001a50: 6974 6820 7377 6565 7073 2061 6e64 2070 ith sweeps and p\n+00001a60: 7574 732e 0a2a 2043 6176 6561 7473 3a3a uts..* Caveats::\n+00001a70: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00001a80: 2020 2020 2057 6865 7265 2074 726f 7562 Where troub\n+00001a90: 6c65 2063 616e 206f 6363 7572 2e0a 0a43 le can occur...C\n+00001aa0: 6176 6561 7473 0a0a 2a20 4c69 6d69 7473 aveats..* Limits\n+00001ab0: 206f 6e20 6572 726f 7220 6465 7465 6374 on error detect\n+00001ac0: 696f 6e3a 3a20 2020 5768 6174 2073 6b65 ion:: What ske\n+00001ad0: 7463 6820 646f 6573 6e27 7420 646f 2e0a tch doesn't do..\n+00001ae0: 2a20 436c 6970 7069 6e67 3a3a 2020 2020 * Clipping:: \n 00001af0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00001b00: 2020 4e6f 2063 6c69 7070 696e 6720 6174 No clipping at\n-00001b10: 2070 7265 7365 6e74 2e0a 2a20 4869 6464 present..* Hidd\n-00001b20: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n-00001b30: 616c 3a3a 2020 2020 2020 496d 7065 7266 al:: Imperf\n-00001b40: 6563 7469 6f6e 7320 746f 2066 6978 2e0a ections to fix..\n-00001b50: 0a48 6964 6465 6e20 7375 7266 6163 6520 .Hidden surface \n-00001b60: 7265 6d6f 7661 6c20 616e 6420 706f 6c79 removal and poly\n-00001b70: 676f 6e20 7370 6c69 7474 696e 670a 0a2a gon splitting..*\n-00001b80: 2053 7461 7469 7374 6963 733a 3a20 2020 Statistics:: \n-00001b90: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-00001ba0: 6572 666f 726d 616e 6365 206e 756d 6265 erformance numbe\n-00001bb0: 7273 206f 6e20 6465 7074 6820 736f 7274 rs on depth sort\n-00001bc0: 2e0a 2a20 4275 6773 2061 6e64 2061 6e6f ..* Bugs and ano\n-00001bd0: 6d61 6c69 6573 3a3a 2020 2020 2020 2020 malies:: \n-00001be0: 2020 496d 7065 7266 6563 7469 6f6e 7320 Imperfections \n-00001bf0: 696e 2074 6869 7320 696d 706c 656d 656e in this implemen\n-00001c00: 7461 7469 6f6e 2e0a 0a0a 1f0a 4669 6c65 tation......File\n-00001c10: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-00001c20: 4e6f 6465 3a20 4162 6f75 7420 736b 6574 Node: About sket\n-00001c30: 6368 2c20 204e 6578 743a 2049 6e74 726f ch, Next: Intro\n-00001c40: 6475 6374 696f 6e20 6279 2065 7861 6d70 duction by examp\n-00001c50: 6c65 2c20 2050 7265 763a 2054 6f70 2c20 le, Prev: Top, \n-00001c60: 2055 703a 2054 6f70 0a0a 3120 4162 6f75 Up: Top..1 Abou\n-00001c70: 7420 736b 6574 6368 0a2a 2a2a 2a2a 2a2a t sketch.*******\n-00001c80: 2a2a 2a2a 2a2a 2a0a 0a2a 204d 656e 753a *******..* Menu:\n-00001c90: 0a0a 2a20 5265 706f 7274 696e 6720 6275 ..* Reporting bu\n-00001ca0: 6773 3a3a 2020 2020 2020 2020 2020 2020 gs:: \n-00001cb0: 2020 4c65 7420 7573 6520 6b6e 6f77 2077 Let use know w\n-00001cc0: 6861 7427 7320 7772 6f6e 6721 0a2a 2043 hat's wrong!.* C\n-00001cd0: 6f6e 7472 6962 7574 696f 6e73 3a3a 2020 ontributions:: \n-00001ce0: 2020 2020 2020 2020 2020 2020 2048 6f77 How\n-00001cf0: 2079 6f75 2063 616e 2068 656c 702e 2e2e you can help...\n-00001d00: 2e0a 0ae2 8098 536b 6574 6368 e280 9920 ......Sketch... \n-00001d10: 6973 2061 2073 6d61 6c6c 2c20 7369 6d70 is a small, simp\n-00001d20: 6c65 2073 7973 7465 6d20 666f 7220 7072 le system for pr\n-00001d30: 6f64 7563 696e 6720 6c69 6e65 2064 7261 oducing line dra\n-00001d40: 7769 6e67 7320 6f66 2074 776f 2d0a 6f72 wings of two-.or\n-00001d50: 2074 6872 6565 2d64 696d 656e 7369 6f6e three-dimension\n-00001d60: 616c 206f 626a 6563 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We\n-00001e40: 2077 616e 7465 6420 746f 2070 726f 6475 wanted to produ\n-00001e50: 6365 2066 696e 656c 790a 7772 6f75 6768 ce finely.wrough\n-00001e60: 742c 206d 6174 6865 6d61 7469 6361 6c6c t, mathematicall\n-00001e70: 792d 6261 7365 6420 696c 6c75 7374 7261 y-based illustra\n-00001e80: 7469 6f6e 7320 7769 7468 206e 6f20 6578 tions with no ex\n-00001e90: 7472 616e 656f 7573 2064 6574 6169 6c2e traneous detail.\n-00001ea0: 0a0a 2020 20e2 8098 536b 6574 6368 e280 .. ...Sketch..\n-00001eb0: 9920 6163 6365 7074 7320 6120 7469 6e79 . accepts a tiny\n-00001ec0: 2073 6365 6e65 2064 6573 6372 6970 7469 scene descripti\n-00001ed0: 6f6e 206c 616e 6775 6167 6520 616e 6420 on language and \n-00001ee0: 6765 6e65 7261 7465 730a e280 9850 5354 generates....PST\n-00001ef0: 7269 636b 73e2 8099 206f 7220 e280 9854 ricks... or ...T\n-00001f00: 696b 5a2f 5047 46e2 8099 2063 6f64 6520 ikZ/PGF... code \n-00001f10: 666f 7220 4c61 5465 582e 2020 5468 6520 for LaTeX. The \n-00001f20: e280 9873 6b65 7463 68e2 8099 206c 616e ...sketch... lan\n-00001f30: 6775 6167 6520 6973 0a73 696d 696c 6172 guage is.similar\n-00001f40: 2074 6f20 e280 9850 5354 7269 636b 73e2 to ...PSTricks.\n-00001f50: 8099 2c20 6d61 6b69 6e67 2069 7420 6561 .., making it ea\n-00001f60: 7379 2074 6f20 6c65 6172 6e20 666f 7220 sy to learn for \n-00001f70: 6375 7272 656e 7420 e280 9850 5354 7269 current ...PSTri\n-00001f80: 636b 73e2 8099 0a75 7365 7273 2e20 2053 cks....users. S\n-00001f90: 6565 2077 7777 2e70 7374 7269 636b 732e ee www.pstricks.\n-00001fa0: 6465 2066 6f72 2069 6e66 6f72 6d61 7469 de for informati\n-00001fb0: 6f6e 206f 6e20 e280 9850 5354 7269 636b on on ...PSTrick\n-00001fc0: 73e2 8099 2e20 20e2 8098 5469 6b5a 2f50 s.... ...TikZ/P\n-00001fd0: 4746 e280 990a 6973 2073 696d 696c 6172 GF....is similar\n-00001fe0: 2e20 2053 6565 2068 7474 703a 2f2f 736f . See http://so\n-00001ff0: 7572 6365 666f 7267 652e 6e65 742f 7072 urceforge.net/pr\n-00002000: 6f6a 6563 7473 2f70 6766 2e20 204f 6e65 ojects/pgf. One\n-00002010: 2063 616e 2065 6173 696c 790a 696e 636c can easily.incl\n-00002020: 7564 6520 6172 6269 7472 6172 7920 e280 ude arbitrary ..\n-00002030: 9850 5354 7269 636b 73e2 8099 206f 7220 .PSTricks... or \n-00002040: e280 9854 696b 5a2f 5047 46e2 8099 2064 ...TikZ/PGF... d\n-00002050: 7261 7769 6e67 7320 616e 6420 7465 7874 rawings and text\n-00002060: 206f 7665 722c 2069 6e2c 0a6f 7220 756e over, in,.or un\n-00002070: 6465 7220 e280 9873 6b65 7463 68e2 8099 der ...sketch...\n-00002080: 2064 7261 7769 6e67 732c 2070 726f 7669 drawings, provi\n-00002090: 6469 6e67 2061 6363 6573 7320 746f 2074 ding access to t\n-000020a0: 6865 2066 756c 6c20 706f 7765 7220 6f66 he full power of\n-000020b0: 204c 6154 6558 0a74 6578 7420 616e 6420 LaTeX.text and \n-000020c0: 6d61 7468 656d 6174 6963 7320 666f 726d mathematics form\n-000020d0: 6174 7469 6e67 2069 6e20 6120 7468 7265 atting in a thre\n-000020e0: 652d 6469 6d65 6e73 696f 6e61 6c20 7365 e-dimensional se\n-000020f0: 7474 696e 672e 0a0a 1f0a 4669 6c65 3a20 tting.....File: \n-00002100: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-00002110: 6465 3a20 5265 706f 7274 696e 6720 6275 de: Reporting bu\n-00002120: 6773 2c20 204e 6578 743a 2043 6f6e 7472 gs, Next: Contr\n-00002130: 6962 7574 696f 6e73 2c20 2050 7265 763a ibutions, Prev:\n-00002140: 2041 626f 7574 2073 6b65 7463 682c 2020 About sketch, \n-00002150: 5570 3a20 4162 6f75 7420 736b 6574 6368 Up: About sketch\n-00002160: 0a0a 312e 3120 5265 706f 7274 696e 6720 ..1.1 Reporting \n-00002170: 6275 6773 2061 6e64 2072 6563 6f6d 6d65 bugs and recomme\n-00002180: 6e64 696e 6720 696d 7072 6f76 656d 656e nding improvemen\n-00002190: 7473 2e0a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ts..============\n+00001b00: 4e6f 2063 6c69 7070 696e 6720 6174 2070 No clipping at p\n+00001b10: 7265 7365 6e74 2e0a 2a20 4869 6464 656e resent..* Hidden\n+00001b20: 2073 7572 6661 6365 2072 656d 6f76 616c surface removal\n+00001b30: 3a3a 2020 2020 2020 496d 7065 7266 6563 :: Imperfec\n+00001b40: 7469 6f6e 7320 746f 2066 6978 2e0a 0a48 tions to fix...H\n+00001b50: 6964 6465 6e20 7375 7266 6163 6520 7265 idden surface re\n+00001b60: 6d6f 7661 6c20 616e 6420 706f 6c79 676f moval and polygo\n+00001b70: 6e20 7370 6c69 7474 696e 670a 0a2a 2053 n splitting..* S\n+00001b80: 7461 7469 7374 6963 733a 3a20 2020 2020 tatistics:: \n+00001b90: 2020 2020 2020 2020 2020 2020 2050 6572 Per\n+00001ba0: 666f 726d 616e 6365 206e 756d 6265 7273 formance numbers\n+00001bb0: 206f 6e20 6465 7074 6820 736f 7274 2e0a on depth sort..\n+00001bc0: 2a20 4275 6773 2061 6e64 2061 6e6f 6d61 * Bugs and anoma\n+00001bd0: 6c69 6573 3a3a 2020 2020 2020 2020 2020 lies:: \n+00001be0: 496d 7065 7266 6563 7469 6f6e 7320 696e Imperfections in\n+00001bf0: 2074 6869 7320 696d 706c 656d 656e 7461 this implementa\n+00001c00: 7469 6f6e 2e0a 0a0a 1f0a 4669 6c65 3a20 tion......File: \n+00001c10: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+00001c20: 6465 3a20 4162 6f75 7420 736b 6574 6368 de: About sketch\n+00001c30: 2c20 204e 6578 743a 2049 6e74 726f 6475 , Next: Introdu\n+00001c40: 6374 696f 6e20 6279 2065 7861 6d70 6c65 ction by example\n+00001c50: 2c20 2050 7265 763a 2054 6f70 2c20 2055 , Prev: Top, U\n+00001c60: 703a 2054 6f70 0a0a 3120 4162 6f75 7420 p: Top..1 About \n+00001c70: 736b 6574 6368 0a2a 2a2a 2a2a 2a2a 2a2a sketch.*********\n+00001c80: 2a2a 2a2a 2a0a 0a2a 204d 656e 753a 0a0a *****..* Menu:..\n+00001c90: 2a20 5265 706f 7274 696e 6720 6275 6773 * Reporting bugs\n+00001ca0: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+00001cb0: 4c65 7420 7573 6520 6b6e 6f77 2077 6861 Let use know wha\n+00001cc0: 7427 7320 7772 6f6e 6721 0a2a 2043 6f6e t's wrong!.* Con\n+00001cd0: 7472 6962 7574 696f 6e73 3a3a 2020 2020 tributions:: \n+00001ce0: 2020 2020 2020 2020 2020 2048 6f77 2079 How y\n+00001cf0: 6f75 2063 616e 2068 656c 702e 2e2e 2e0a ou can help.....\n+00001d00: 0ae2 8098 536b 6574 6368 e280 9920 6973 ....Sketch... is\n+00001d10: 2061 2073 6d61 6c6c 2c20 7369 6d70 6c65 a small, simple\n+00001d20: 2073 7973 7465 6d20 666f 7220 7072 6f64 system for prod\n+00001d30: 7563 696e 6720 6c69 6e65 2064 7261 7769 ucing line drawi\n+00001d40: 6e67 7320 6f66 2074 776f 2d0a 6f72 2074 ngs of two-.or t\n+00001d50: 6872 6565 2d64 696d 656e 7369 6f6e 616c hree-dimensional\n+00001d60: 206f 626a 6563 7473 2061 6e64 2073 6365 objects and sce\n+00001d70: 6e65 732e 2020 4974 2062 6567 616e 2061 nes. It began a\n+00001d80: 7320 6120 7761 7920 746f 206d 616b 650a s a way to make.\n+00001d90: 696c 6c75 7374 7261 7469 6f6e 7320 666f illustrations fo\n+00001da0: 7220 6120 7465 7874 626f 6f6b 2061 6674 r a textbook aft\n+00001db0: 6572 2077 6520 636f 756c 6420 6669 6e64 er we could find\n+00001dc0: 206e 6f20 7375 6974 6162 6c65 2074 6f6f no suitable too\n+00001dd0: 6c20 666f 720a 7468 6973 2070 7572 706f l for.this purpo\n+00001de0: 7365 2e20 2045 7869 7374 696e 6720 7363 se. Existing sc\n+00001df0: 656e 6520 7072 6f63 6573 736f 7273 2065 ene processors e\n+00001e00: 6d70 6861 7369 7a65 6420 4755 4973 2061 mphasized GUIs a\n+00001e10: 6e64 2f6f 720a 7068 6f74 6f2d 7265 616c nd/or.photo-real\n+00001e20: 6973 6d2c 2062 6f74 6820 756e 2d75 7365 ism, both un-use\n+00001e30: 6675 6c20 746f 2075 732e 2020 5765 2077 ful to us. We w\n+00001e40: 616e 7465 6420 746f 2070 726f 6475 6365 anted to produce\n+00001e50: 2066 696e 656c 790a 7772 6f75 6768 742c finely.wrought,\n+00001e60: 206d 6174 6865 6d61 7469 6361 6c6c 792d mathematically-\n+00001e70: 6261 7365 6420 696c 6c75 7374 7261 7469 based illustrati\n+00001e80: 6f6e 7320 7769 7468 206e 6f20 6578 7472 ons with no extr\n+00001e90: 616e 656f 7573 2064 6574 6169 6c2e 0a0a aneous detail...\n+00001ea0: 2020 20e2 8098 536b 6574 6368 e280 9920 ...Sketch... \n+00001eb0: 6163 6365 7074 7320 6120 7469 6e79 2073 accepts a tiny s\n+00001ec0: 6365 6e65 2064 6573 6372 6970 7469 6f6e cene description\n+00001ed0: 206c 616e 6775 6167 6520 616e 6420 6765 language and ge\n+00001ee0: 6e65 7261 7465 730a e280 9850 5354 7269 nerates....PSTri\n+00001ef0: 636b 73e2 8099 206f 7220 e280 9854 696b cks... or ...Tik\n+00001f00: 5a2f 5047 46e2 8099 2063 6f64 6520 666f Z/PGF... code fo\n+00001f10: 7220 4c61 5465 582e 2020 5468 6520 e280 r LaTeX. The ..\n+00001f20: 9873 6b65 7463 68e2 8099 206c 616e 6775 .sketch... langu\n+00001f30: 6167 6520 6973 0a73 696d 696c 6172 2074 age is.similar t\n+00001f40: 6f20 e280 9850 5354 7269 636b 73e2 8099 o ...PSTricks...\n+00001f50: 2c20 6d61 6b69 6e67 2069 7420 6561 7379 , making it easy\n+00001f60: 2074 6f20 6c65 6172 6e20 666f 7220 6375 to learn for cu\n+00001f70: 7272 656e 7420 e280 9850 5354 7269 636b rrent ...PSTrick\n+00001f80: 73e2 8099 0a75 7365 7273 2e20 2053 6565 s....users. See\n+00001f90: 2077 7777 2e70 7374 7269 636b 732e 6465 www.pstricks.de\n+00001fa0: 2066 6f72 2069 6e66 6f72 6d61 7469 6f6e for information\n+00001fb0: 206f 6e20 e280 9850 5354 7269 636b 73e2 on ...PSTricks.\n+00001fc0: 8099 2e20 20e2 8098 5469 6b5a 2f50 4746 ... ...TikZ/PGF\n+00001fd0: e280 990a 6973 2073 696d 696c 6172 2e20 ....is similar. \n+00001fe0: 2053 6565 2068 7474 703a 2f2f 736f 7572 See http://sour\n+00001ff0: 6365 666f 7267 652e 6e65 742f 7072 6f6a ceforge.net/proj\n+00002000: 6563 7473 2f70 6766 2e20 204f 6e65 2063 ects/pgf. One c\n+00002010: 616e 2065 6173 696c 790a 696e 636c 7564 an easily.includ\n+00002020: 6520 6172 6269 7472 6172 7920 e280 9850 e arbitrary ...P\n+00002030: 5354 7269 636b 73e2 8099 206f 7220 e280 STricks... or ..\n+00002040: 9854 696b 5a2f 5047 46e2 8099 2064 7261 .TikZ/PGF... dra\n+00002050: 7769 6e67 7320 616e 6420 7465 7874 206f wings and text o\n+00002060: 7665 722c 2069 6e2c 0a6f 7220 756e 6465 ver, in,.or unde\n+00002070: 7220 e280 9873 6b65 7463 68e2 8099 2064 r ...sketch... d\n+00002080: 7261 7769 6e67 732c 2070 726f 7669 6469 rawings, providi\n+00002090: 6e67 2061 6363 6573 7320 746f 2074 6865 ng access to the\n+000020a0: 2066 756c 6c20 706f 7765 7220 6f66 204c full power of L\n+000020b0: 6154 6558 0a74 6578 7420 616e 6420 6d61 aTeX.text and ma\n+000020c0: 7468 656d 6174 6963 7320 666f 726d 6174 thematics format\n+000020d0: 7469 6e67 2069 6e20 6120 7468 7265 652d ting in a three-\n+000020e0: 6469 6d65 6e73 696f 6e61 6c20 7365 7474 dimensional sett\n+000020f0: 696e 672e 0a0a 1f0a 4669 6c65 3a20 736b ing.....File: sk\n+00002100: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+00002110: 3a20 5265 706f 7274 696e 6720 6275 6773 : Reporting bugs\n+00002120: 2c20 204e 6578 743a 2043 6f6e 7472 6962 , Next: Contrib\n+00002130: 7574 696f 6e73 2c20 2050 7265 763a 2041 utions, Prev: A\n+00002140: 626f 7574 2073 6b65 7463 682c 2020 5570 bout sketch, Up\n+00002150: 3a20 4162 6f75 7420 736b 6574 6368 0a0a : About sketch..\n+00002160: 312e 3120 5265 706f 7274 696e 6720 6275 1.1 Reporting bu\n+00002170: 6773 2061 6e64 2072 6563 6f6d 6d65 6e64 gs and recommend\n+00002180: 696e 6720 696d 7072 6f76 656d 656e 7473 ing improvements\n+00002190: 2e0a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ..==============\n 000021a0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n 000021b0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-000021c0: 3d3d 3d3d 3d0a 0a54 6865 2067 726f 7570 =====..The group\n-000021d0: 2068 7474 703a 2f2f 6772 6f75 7073 2e67 http://groups.g\n-000021e0: 6f6f 676c 652e 636f 6d2f 6772 6f75 702f oogle.com/group/\n-000021f0: 736b 6574 6368 2d75 7365 7273 2069 7320 sketch-users is \n-00002200: 7468 6520 6265 7374 2070 6c61 6365 0a74 the best place.t\n-00002210: 6f20 7265 706f 7274 2062 7567 7320 616e o report bugs an\n-00002220: 6420 6d61 6b65 2069 6d70 726f 7665 6d65 d make improveme\n-00002230: 6e74 732e 2020 4120 7365 636f 6e64 206d nts. A second m\n-00002240: 6574 686f 6420 7468 6174 2077 696c 6c0a ethod that will.\n-00002250: 7072 6f62 6162 6c79 2070 726f 6475 6365 probably produce\n-00002260: 2061 2073 6c6f 7765 7220 7265 7370 6f6e a slower respon\n-00002270: 7365 2069 7320 656d 6169 6c20 746f 2073 se is email to s\n-00002280: 6b65 7463 6840 6672 6f6e 7469 6572 6e65 ketch@frontierne\n-00002290: 742e 6e65 742e 0a57 6520 7769 6c6c 2074 t.net..We will t\n-000022a0: 7279 2074 6f20 7265 7370 6f6e 642c 2062 ry to respond, b\n-000022b0: 7574 2063 616e 2774 2070 726f 6d69 7365 ut can't promise\n-000022c0: 2e20 2049 6e20 616e 7920 6576 656e 742c . In any event,\n-000022d0: 2064 6f6e 2774 2062 650a 6f66 6665 6e64 don't be.offend\n-000022e0: 6564 2069 6620 6120 7265 706c 7920 6973 ed if a reply is\n-000022f0: 206e 6f74 2066 6f72 7468 636f 6d69 6e67 not forthcoming\n-00002300: 2e20 2057 6527 7265 206a 7573 7420 6275 . We're just bu\n-00002310: 7379 2061 6e64 2077 696c 6c20 6765 7420 sy and will get \n-00002320: 746f 0a79 6f75 7220 7375 6767 6573 7469 to.your suggesti\n-00002330: 6f6e 2065 7665 6e74 7561 6c6c 792e 0a0a on eventually...\n-00002340: 2020 2046 6f72 2062 7567 732c 2061 7474 For bugs, att\n-00002350: 6163 6820 6120 e280 9873 6b65 7463 68e2 ach a ...sketch.\n-00002360: 8099 2069 6e70 7574 2066 696c 6520 7468 .. input file th\n-00002370: 6174 2063 6175 7365 7320 7468 6520 6261 at causes the ba\n-00002380: 6420 6265 6861 7669 6f72 2e0a 456d 6265 d behavior..Embe\n-00002390: 6420 636f 6d6d 656e 7473 2074 6861 7420 d comments that \n-000023a0: 6578 706c 6169 6e20 7768 6174 2074 6f20 explain what to \n-000023b0: 6c6f 6f6b 2066 6f72 2069 6e20 7468 6520 look for in the \n-000023c0: 6265 6861 7669 6f72 206f 6620 e280 9873 behavior of ...s\n-000023d0: 6b65 7463 68e2 8099 0a6f 7220 6974 7320 ketch....or its \n-000023e0: 6f75 7470 7574 2e0a 0a20 2020 4120 7265 output... A re\n-000023f0: 636f 6d6d 656e 6461 7469 6f6e 2066 6f72 commendation for\n-00002400: 2069 6d70 726f 7665 6d65 6e74 2066 726f improvement fro\n-00002410: 6d20 6f6e 6520 756e 6b6e 6f77 6e20 7065 m one unknown pe\n-00002420: 7273 6f6e 2063 6f75 6e74 7320 6173 0a6f rson counts as.o\n-00002430: 6e65 2076 6f74 652e 2020 5765 2075 7365 ne vote. We use\n-00002440: 206f 7665 7261 6c6c 2076 6f74 6520 7461 overall vote ta\n-00002450: 6c6c 6965 7320 746f 2064 6563 6964 6520 llies to decide \n-00002460: 7768 6174 2074 6f20 646f 206e 6578 7420 what to do next \n-00002470: 6173 0a72 6573 6f75 7263 6573 2070 6572 as.resources per\n-00002480: 6d69 742e 2020 5765 2072 6573 6572 7665 mit. We reserve\n-00002490: 2074 6865 2072 6967 6874 2074 6f20 6173 the right to as\n-000024a0: 7369 676e 2061 6e79 206e 756d 6265 7220 sign any number \n-000024b0: 6f66 2076 6f74 6573 2074 6f0a 7375 6767 of votes to.sugg\n-000024c0: 6573 7469 6f6e 7320 6672 6f6d 2070 656f estions from peo\n-000024d0: 706c 6520 7768 6f20 6861 7665 2062 6565 ple who have bee\n-000024e0: 6e20 6865 6c70 6675 6c20 616e 6420 7375 n helpful and su\n-000024f0: 7070 6f72 7469 7665 2069 6e20 7468 650a pportive in the.\n-00002500: 7061 7374 2e0a 0a1f 0a46 696c 653a 2073 past.....File: s\n-00002510: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n-00002520: 653a 2043 6f6e 7472 6962 7574 696f 6e73 e: Contributions\n-00002530: 2c20 2050 7265 763a 2052 6570 6f72 7469 , Prev: Reporti\n-00002540: 6e67 2062 7567 732c 2020 5570 3a20 4162 ng bugs, Up: Ab\n-00002550: 6f75 7420 736b 6574 6368 0a0a 312e 3220 out sketch..1.2 \n-00002560: 436f 6e74 7269 6275 7469 6f6e 730a 3d3d Contributions.==\n-00002570: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a ===============.\n-00002580: 0a49 6620 796f 7520 696e 7465 6e64 2074 .If you intend t\n-00002590: 6f20 696d 706c 656d 656e 7420 616e 2065 o implement an e\n-000025a0: 6e68 616e 6365 6d65 6e74 206f 6620 796f nhancement of yo\n-000025b0: 7572 206f 776e 2c20 7468 6174 2773 2074 ur own, that's t\n-000025c0: 6572 7269 6669 6321 0a43 6f6e 7369 6465 errific!.Conside\n-000025d0: 7220 636f 6c6c 6162 6f72 6174 696e 6720 r collaborating \n-000025e0: 7769 7468 2075 7320 6669 7273 7420 746f with us first to\n-000025f0: 2073 6565 2069 6620 7765 2772 6520 616c see if we're al\n-00002600: 7265 6164 7920 776f 726b 696e 6720 6f6e ready working on\n-00002610: 0a79 6f75 7220 6964 6561 206f 7220 6966 .your idea or if\n-00002620: 2077 6520 6361 6e20 7573 6520 796f 7572 we can use your\n-00002630: 2077 6f72 6b20 696e 2074 6865 206f 6666 work in the off\n-00002640: 6963 6961 6c20 7265 6c65 6173 652e 0a0a icial release...\n-00002650: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n-00002660: 3030 302e 706e 6722 2074 6578 743d 2249 000.png\" text=\"I\n-00002670: 6d61 6765 2065 7830 3030 206f 6d69 7474 mage ex000 omitt\n-00002680: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n-00002690: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n-000026a0: 656e 742e 2200 085d 0a0a 1f0a 4669 6c65 ent.\"..]....File\n-000026b0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-000026c0: 4e6f 6465 3a20 496e 7472 6f64 7563 7469 Node: Introducti\n-000026d0: 6f6e 2062 7920 6578 616d 706c 652c 2020 on by example, \n-000026e0: 4e65 7874 3a20 496e 7075 7420 6c61 6e67 Next: Input lang\n-000026f0: 7561 6765 2c20 2050 7265 763a 2041 626f uage, Prev: Abo\n-00002700: 7574 2073 6b65 7463 682c 2020 5570 3a20 ut sketch, Up: \n-00002710: 546f 700a 0a32 2049 6e74 726f 6475 6374 Top..2 Introduct\n-00002720: 696f 6e20 6279 2065 7861 6d70 6c65 0a2a ion by example.*\n+000021c0: 3d3d 3d0a 0a54 6865 2067 726f 7570 2068 ===..The group h\n+000021d0: 7474 703a 2f2f 6772 6f75 7073 2e67 6f6f ttp://groups.goo\n+000021e0: 676c 652e 636f 6d2f 6772 6f75 702f 736b gle.com/group/sk\n+000021f0: 6574 6368 2d75 7365 7273 2069 7320 7468 etch-users is th\n+00002200: 6520 6265 7374 2070 6c61 6365 0a74 6f20 e best place.to \n+00002210: 7265 706f 7274 2062 7567 7320 616e 6420 report bugs and \n+00002220: 6d61 6b65 2069 6d70 726f 7665 6d65 6e74 make improvement\n+00002230: 732e 2020 4120 7365 636f 6e64 206d 6574 s. A second met\n+00002240: 686f 6420 7468 6174 2077 696c 6c0a 7072 hod that will.pr\n+00002250: 6f62 6162 6c79 2070 726f 6475 6365 2061 obably produce a\n+00002260: 2073 6c6f 7765 7220 7265 7370 6f6e 7365 slower response\n+00002270: 2069 7320 656d 6169 6c20 746f 2073 6b65 is email to ske\n+00002280: 7463 6840 6672 6f6e 7469 6572 6e65 742e tch@frontiernet.\n+00002290: 6e65 742e 0a57 6520 7769 6c6c 2074 7279 net..We will try\n+000022a0: 2074 6f20 7265 7370 6f6e 642c 2062 7574 to respond, but\n+000022b0: 2063 616e 2774 2070 726f 6d69 7365 2e20 can't promise. \n+000022c0: 2049 6e20 616e 7920 6576 656e 742c 2064 In any event, d\n+000022d0: 6f6e 2774 2062 650a 6f66 6665 6e64 6564 on't be.offended\n+000022e0: 2069 6620 6120 7265 706c 7920 6973 206e if a reply is n\n+000022f0: 6f74 2066 6f72 7468 636f 6d69 6e67 2e20 ot forthcoming. \n+00002300: 2057 6527 7265 206a 7573 7420 6275 7379 We're just busy\n+00002310: 2061 6e64 2077 696c 6c20 6765 7420 746f and will get to\n+00002320: 0a79 6f75 7220 7375 6767 6573 7469 6f6e .your suggestion\n+00002330: 2065 7665 6e74 7561 6c6c 792e 0a0a 2020 eventually... \n+00002340: 2046 6f72 2062 7567 732c 2061 7474 6163 For bugs, attac\n+00002350: 6820 6120 e280 9873 6b65 7463 68e2 8099 h a ...sketch...\n+00002360: 2069 6e70 7574 2066 696c 6520 7468 6174 input file that\n+00002370: 2063 6175 7365 7320 7468 6520 6261 6420 causes the bad \n+00002380: 6265 6861 7669 6f72 2e0a 456d 6265 6420 behavior..Embed \n+00002390: 636f 6d6d 656e 7473 2074 6861 7420 6578 comments that ex\n+000023a0: 706c 6169 6e20 7768 6174 2074 6f20 6c6f plain what to lo\n+000023b0: 6f6b 2066 6f72 2069 6e20 7468 6520 6265 ok for in the be\n+000023c0: 6861 7669 6f72 206f 6620 e280 9873 6b65 havior of ...ske\n+000023d0: 7463 68e2 8099 0a6f 7220 6974 7320 6f75 tch....or its ou\n+000023e0: 7470 7574 2e0a 0a20 2020 4120 7265 636f tput... 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2a2a 0a0a 5468 6520 e280 ********..The ..\n-00002750: 9873 6b65 7463 68e2 8099 2069 6e70 7574 .sketch... input\n-00002760: 206c 616e 6775 6167 6520 7769 6c6c 2073 language will s\n-00002770: 6565 6d20 6661 6d69 6c69 6172 2074 6f20 eem familiar to \n-00002780: 7573 6572 7320 6f66 2074 6865 0ae2 8098 users of the....\n-00002790: 5053 5472 6963 6b73 e280 9920 7061 636b PSTricks... pack\n-000027a0: 6167 6520 666f 7220 4c61 5465 582e 2020 age for LaTeX. \n-000027b0: 5468 6520 666f 6c6c 6f77 696e 6720 7072 The following pr\n-000027c0: 6f67 7261 6d20 6472 6177 7320 6120 7472 ogram draws a tr\n-000027d0: 6961 6e67 756c 6172 0a70 6f6c 7967 6f6e iangular.polygon\n-000027e0: 2070 6965 7263 6564 2062 7920 6120 6c69 pierced by a li\n-000027f0: 6e65 2e0a 2020 706f 6c79 676f 6e28 302c ne.. polygon(0,\n-00002800: 302c 3129 2831 2c30 2c30 2928 302c 312c 0,1)(1,0,0)(0,1,\n-00002810: 3029 0a20 206c 696e 6528 2d31 2c2d 312c 0). line(-1,-1,\n-00002820: 2d31 2928 322c 322c 3229 0a54 6865 2063 -1)(2,2,2).The 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Th\n+000027b0: 6520 666f 6c6c 6f77 696e 6720 7072 6f67 e following prog\n+000027c0: 7261 6d20 6472 6177 7320 6120 7472 6961 ram draws a tria\n+000027d0: 6e67 756c 6172 0a70 6f6c 7967 6f6e 2070 ngular.polygon p\n+000027e0: 6965 7263 6564 2062 7920 6120 6c69 6e65 ierced by a line\n+000027f0: 2e0a 2020 706f 6c79 676f 6e28 302c 302c .. polygon(0,0,\n+00002800: 3129 2831 2c30 2c30 2928 302c 312c 3029 1)(1,0,0)(0,1,0)\n+00002810: 0a20 206c 696e 6528 2d31 2c2d 312c 2d31 . line(-1,-1,-1\n+00002820: 2928 322c 322c 3229 0a54 6865 2063 6f6f )(2,2,2).The coo\n+00002830: 7264 696e 6174 6520 7379 7374 656d 2069 rdinate system i\n+00002840: 7320 6120 7374 616e 6461 7264 2072 6967 s a standard rig\n+00002850: 6874 2d68 616e 6465 6420 4361 7274 6573 ht-handed Cartes\n+00002860: 6961 6e20 6f6e 652e 0a0a 0008 5b69 6d61 ian one.....[ima\n+00002870: 6765 2073 7263 3d22 6578 3031 302e 706e ge src=\"ex010.pn\n+00002880: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+00002890: 7830 3130 206f 6d69 7474 6564 2069 6e20 x010 omitted in \n+000028a0: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+000028b0: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+000028c0: 085d 0a0a 2a20 4d65 6e75 3a0a 0a2a 2048 .]..* Menu:..* H\n+000028d0: 656c 6c6f 2077 6f72 6c64 3a3a 2020 2020 ello world:: \n+000028e0: 2020 2020 2020 2020 2020 2020 2053 696d Sim\n+000028f0: 706c 6573 7420 706f 7373 6962 6c65 20e2 plest possible .\n+00002900: 8098 736b 6574 6368 e280 9920 7072 6f67 ..sketch... prog\n+00002910: 7261 6d2e 0a2a 2044 7261 7769 6e67 206f ram..* Drawing o\n+00002920: 7074 696f 6e73 3a3a 2020 2020 2020 2020 ptions:: \n+00002930: 2020 2020 2043 6f6e 7472 6f6c 6c69 6e67 Controlling\n+00002940: 206f 626a 6563 7420 6170 7065 6172 616e object appearan\n+00002950: 6365 2e0a 2a20 4472 6177 696e 6720 6120 ce..* Drawing a \n+00002960: 736f 6c69 643a 3a20 2020 2020 2020 2020 solid:: \n+00002970: 2020 2020 4472 6177 696e 6720 616e 206f Drawing an o\n+00002980: 626a 6563 7420 7769 7468 2033 6420 6170 bject with 3d ap\n+00002990: 7065 6172 616e 6365 2e0a 2a20 5370 6563 pearance..* Spec\n+000029a0: 6961 6c20 6f62 6a65 6374 733a 3a20 2020 ial objects:: \n+000029b0: 2020 2020 2020 2020 2020 4c61 7969 6e67 Laying\n+000029c0: 2054 6558 206f 7665 722c 2069 6e2c 206f TeX over, in, o\n+000029d0: 7220 756e 6465 7220 6472 6177 696e 6773 r under drawings\n+000029e0: 2e0a 2a20 4f62 6a65 6374 2074 7261 6e73 ..* Object trans\n+000029f0: 666f 726d 733a 3a20 2020 2020 2020 2020 forms:: \n+00002a00: 2020 526f 7461 7465 2c20 7472 616e 736c Rotate, transl\n+00002a10: 6174 652c 2073 6361 6c65 2c20 616e 6420 ate, scale, and \n+00002a20: 6f74 6865 7273 2e0a 2a20 5265 7065 6174 others..* Repeat\n+00002a30: 6564 206f 626a 6563 7473 3a3a 2020 2020 ed objects:: \n+00002a40: 2020 2020 2020 2020 4d61 6b69 6e67 2074 Making t\n+00002a50: 7261 6e73 666f 726d 6564 2063 6f70 6965 ransformed copie\n+00002a60: 732e 0a2a 2053 7765 7074 206f 626a 6563 s..* Swept objec\n+00002a70: 7473 3a3a 2020 2020 2020 2020 2020 2020 ts:: \n+00002a80: 2020 2053 7765 6570 696e 6720 6f62 6a65 Sweeping obje\n+00002a90: 6374 7320 696e 2073 7061 6365 2074 6f20 cts in space to \n+00002aa0: 6d61 6b65 206e 6577 2073 6861 7065 732e make new shapes.\n+00002ab0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n+00002ac0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4865 .info, Node: He\n+00002ad0: 6c6c 6f20 776f 726c 642c 2020 4e65 7874 llo world, Next\n+00002ae0: 3a20 4472 6177 696e 6720 6f70 7469 6f6e : Drawing option\n+00002af0: 732c 2020 5072 6576 3a20 496e 7472 6f64 s, Prev: Introd\n+00002b00: 7563 7469 6f6e 2062 7920 6578 616d 706c uction by exampl\n+00002b10: 652c 2020 5570 3a20 496e 7472 6f64 7563 e, Up: Introduc\n+00002b20: 7469 6f6e 2062 7920 6578 616d 706c 650a tion by example.\n+00002b30: 0a32 2e31 2048 656c 6c6f 2077 6f72 6c64 .2.1 Hello world\n+00002b40: 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d .===============\n+00002b50: 0a0a 5468 6520 e280 9873 6b65 7463 68e2 ..The ...sketch.\n+00002b60: 8099 2070 726f 6772 616d 2061 626f 7665 .. program above\n+00002b70: 2069 7320 6e65 6172 6c79 2074 6865 2073 is nearly the s\n+00002b80: 696d 706c 6573 7420 6f6e 6520 706f 7373 implest one poss\n+00002b90: 6962 6c65 2c20 7468 650a 6571 7569 7661 ible, the.equiva\n+00002ba0: 6c65 6e74 206f 6620 6120 2268 656c 6c6f lent of a \"hello\n+00002bb0: 2077 6f72 6c64 2220 7072 6f67 7261 6d20 world\" program \n+00002bc0: 796f 7520 6d69 6768 7420 6669 6e64 2061 you might find a\n+00002bd0: 7420 7468 6520 7374 6172 7420 6f66 2061 t the start of a\n+00002be0: 0a70 726f 6772 616d 6d69 6e67 206c 616e .programming lan\n+00002bf0: 6775 6167 6520 7465 7874 2e20 2049 6620 guage text. 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T\n+00002cc0: 6865 2063 6f6e 7465 6e74 7320 6f66 20e2 he contents of .\n+00002cd0: 8098 7369 6d70 6c65 2e74 6578 e280 9920 ..simple.tex... \n+00002ce0: 6c6f 6f6b 206c 696b 6520 7468 6973 2e0a look like this..\n+00002cf0: 2020 5c62 6567 696e 7b70 7370 6963 7475 \\begin{pspictu\n+00002d00: 7265 7d28 2d31 2c2d 3129 2832 2c32 290a re}(-1,-1)(2,2).\n+00002d10: 2020 5c70 7374 5665 7262 7b31 2073 6574 \\pstVerb{1 set\n+00002d20: 6c69 6e65 6a6f 696e 7d0a 2020 5c70 736c linejoin}. \\psl\n+00002d30: 696e 6528 2d31 2c2d 3129 282e 3333 332c ine(-1,-1)(.333,\n+00002d40: 2e33 3333 290a 2020 5c70 7370 6f6c 7967 .333). \\pspolyg\n+00002d50: 6f6e 5b66 696c 6c73 7479 6c65 3d73 6f6c on[fillstyle=sol\n+00002d60: 6964 2c66 696c 6c63 6f6c 6f72 3d77 6869 id,fillcolor=whi\n+00002d70: 7465 5d28 302c 3029 2831 2c30 2928 302c te](0,0)(1,0)(0,\n+00002d80: 3129 0a20 205c 7073 6c69 6e65 282e 3333 1). \\psline(.33\n+00002d90: 332c 2e33 3333 2928 322c 3229 0a20 205c 3,.333)(2,2). \\\n+00002da0: 656e 647b 7073 7069 6374 7572 657d 0a54 end{pspicture}.T\n+00002db0: 6865 2068 6964 6465 6e20 7375 7266 6163 he hidden surfac\n+00002dc0: 6520 616c 676f 7269 7468 6d20 6f66 20e2 e algorithm of .\n+00002dd0: 8098 736b 6574 6368 e280 9920 6861 7320 ..sketch... has \n+00002de0: 7370 6c69 7420 7468 6520 6c69 6e65 2069 split the line i\n+00002df0: 6e74 6f20 7477 6f0a 7069 6563 6573 2061 nto two.pieces a\n+00002e00: 6e64 206f 7264 6572 6564 2074 6865 2074 nd ordered the t\n+00002e10: 6872 6565 2072 6573 756c 7469 6e67 206f hree resulting o\n+00002e20: 626a 6563 7473 2073 6f20 7468 6174 2074 bjects so that t\n+00002e30: 6865 2063 6f72 7265 6374 0a70 6f72 7469 he correct.porti\n+00002e40: 6f6e 206f 6620 7468 6520 6c69 6e65 2069 on of the line i\n+00002e50: 7320 6869 6464 656e 2e0a 0a20 2020 4966 s hidden... If\n+00002e60: 2079 6f75 2776 6520 6e6f 7469 6365 6420 you've noticed \n+00002e70: 7468 6174 2074 6865 2070 726f 6a65 6374 that the project\n+00002e80: 696f 6e20 7765 2061 7265 2075 7369 6e67 ion we are using\n+00002e90: 2073 6565 6d73 2065 7175 6976 616c 656e seems equivalen\n+00002ea0: 740a 746f 2065 7261 7369 6e67 2074 6865 t.to erasing the\n+00002eb0: 207a 2d63 6f6f 7264 696e 6174 6520 6f66 z-coordinate of\n+00002ec0: 2074 6865 2074 6872 6565 2d64 696d 656e the three-dimen\n+00002ed0: 7369 6f6e 616c 2069 6e70 7574 2070 6f69 sional input poi\n+00002ee0: 6e74 732c 2070 6174 0a79 6f75 7273 656c nts, pat.yoursel\n+00002ef0: 6620 6f6e 2074 6865 2062 6163 6b2e 2020 f on the back. \n+00002f00: 596f 7520 6172 6520 636f 7272 6563 742e You are correct.\n+00002f10: 2020 5468 6973 2069 7320 6361 6c6c 6564 This is called\n+00002f20: 2061 20e2 809c 7061 7261 6c6c 656c 0a70 a ...parallel.p\n+00002f30: 726f 6a65 6374 696f 6ee2 809d 2e20 2054 rojection.... 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Alternate\n+00003020: 6c79 2c20 6164 6469 6e67 2074 6865 2063 ly, adding the c\n+00003030: 6f6d 6d61 6e64 206c 696e 6520 6f70 7469 ommand line opti\n+00003040: 6f6e 20e2 8098 2d54 e280 9928 3129 0a63 on ...-T...(1).c\n+00003050: 6175 7365 7320 7468 6520 e280 9870 7370 auses the ...psp\n+00003060: 6963 7475 7265 e280 9920 746f 2062 6520 icture... to be \n+00003070: 7772 6170 7065 6420 696e 2061 2073 686f wrapped in a sho\n+00003080: 7274 2062 7574 2063 6f6d 706c 6574 6520 rt but complete \n+00003090: 646f 6375 6d65 6e74 2c0a 7265 6164 7920 document,.ready \n+000030a0: 746f 2072 756e 2074 686f 7567 6820 4c61 to run though La\n+000030b0: 5465 582e 2020 496e 2061 2066 696e 6973 TeX. In a finis\n+000030c0: 6865 642c 2074 7970 6573 6574 2064 6f63 hed, typeset doc\n+000030d0: 756d 656e 742c 2074 6865 2070 6963 7475 ument, the pictu\n+000030e0: 7265 0a6c 6f6f 6b73 206c 696b 6520 7468 re.looks like th\n+000030f0: 6973 2e20 2028 5468 6520 6178 6573 2068 is. (The axes h\n+00003100: 6176 6520 6265 656e 2061 6464 6564 2069 ave been added i\n+00003110: 6e20 6c69 6768 7420 6772 6179 2e29 0a0a n light gray.)..\n+00003120: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n+00003130: 3032 302e 706e 6722 2074 6578 743d 2249 020.png\" text=\"I\n+00003140: 6d61 6765 2065 7830 3230 206f 6d69 7474 mage ex020 omitt\n+00003150: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n+00003160: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n+00003170: 656e 742e 2200 085d 0a0a 4974 2069 7320 ent.\"..]..It is \n+00003180: 696d 706f 7274 616e 7420 746f 206b 6e6f important to kno\n+00003190: 7720 7468 6174 206f 6e6c 7920 7468 6520 w that only the \n+000031a0: 226f 7574 7369 6465 2220 6f66 2061 2070 \"outside\" of a p\n+000031b0: 6f6c 7967 6f6e 2069 7320 6e6f 726d 616c olygon is normal\n+000031c0: 6c79 0a64 7261 776e 2e20 2054 6865 20e2 ly.drawn. The .\n+000031d0: 809c 6f75 7473 6964 65e2 809d 2069 7320 ..outside... is \n+000031e0: 7768 6572 6520 7468 6520 7665 7274 6963 where the vertic\n+000031f0: 6573 2067 6976 656e 2069 6e20 7468 6520 es given in the \n+00003200: e280 9870 6f6c 7967 6f6e e280 990a 636f ...polygon....co\n+00003210: 6d6d 616e 6420 6170 7065 6172 2069 6e20 mmand appear in \n+00003220: 5f63 6f75 6e74 6572 2d63 6c6f 636b 7769 _counter-clockwi\n+00003230: 7365 5f20 6f72 6465 722e 2020 5468 7573 se_ order. Thus\n+00003240: 2c20 6966 2074 6865 2063 6f6d 6d61 6e64 , if the command\n+00003250: 2061 626f 7665 0a68 6164 2062 6565 6e0a above.had been.\n+00003260: 2020 706f 6c79 676f 6e28 302c 312c 3029 polygon(0,1,0)\n+00003270: 2831 2c30 2c30 2928 302c 302c 3129 0a74 (1,0,0)(0,0,1).t\n+00003280: 6865 2070 6f6c 7967 6f6e 2077 6f75 6c64 he polygon would\n+00003290: 206e 6f74 2061 7070 6561 7220 696e 2074 not appear in t\n+000032a0: 6865 2070 6963 7475 7265 2061 7420 616c he picture at al\n+000032b0: 6c2e 2020 4974 2077 6f75 6c64 2068 6176 l. It would hav\n+000032c0: 6520 6265 656e 0ae2 809c 6375 6c6c 6564 e been....culled\n+000032d0: e280 9d20 6672 6f6d 2074 6865 2073 6365 ... from the sce\n+000032e0: 6e65 2e20 2054 6869 7320 6375 6c6c 696e ne. This cullin\n+000032f0: 6720 6265 6861 7669 6f72 206d 6179 2073 g behavior may s\n+00003300: 6565 6d20 7374 7261 6e67 652c 2062 7574 eem strange, but\n+00003310: 0a73 7461 7920 7475 6e65 642e 0a0a 2020 .stay tuned... \n+00003320: 202d 2d2d 2d2d 2d2d 2d2d 2d20 466f 6f74 ---------- Foot\n+00003330: 6e6f 7465 7320 2d2d 2d2d 2d2d 2d2d 2d2d notes ----------\n+00003340: 0a0a 2020 2028 3129 204f 7220 666f 7220 .. (1) Or for \n+00003350: 4575 726f 7065 616e 2075 7365 7273 206f European users o\n+00003360: 6620 4134 2073 697a 6520 7061 7065 722c f A4 size paper,\n+00003370: 20e2 8098 2d54 65e2 8099 2e0a 0a1f 0a46 ...-Te........F\n+00003380: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+00003390: 2c20 204e 6f64 653a 2044 7261 7769 6e67 , Node: Drawing\n+000033a0: 206f 7074 696f 6e73 2c20 204e 6578 743a options, Next:\n+000033b0: 2044 7261 7769 6e67 2061 2073 6f6c 6964 Drawing a solid\n+000033c0: 2c20 2050 7265 763a 2048 656c 6c6f 2077 , Prev: Hello w\n+000033d0: 6f72 6c64 2c20 2055 703a 2049 6e74 726f orld, Up: Intro\n+000033e0: 6475 6374 696f 6e20 6279 2065 7861 6d70 duction by examp\n+000033f0: 6c65 0a0a 322e 3220 4f70 7469 6f6e 730a le..2.2 Options.\n+00003400: 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0a4d 616e ===========..Man\n+00003410: 7920 e280 9850 5354 7269 636b 73e2 8099 y ...PSTricks...\n+00003420: 2061 6e64 20e2 8098 5469 6b5a 2f50 4746 and ...TikZ/PGF\n+00003430: e280 9920 6f70 7469 6f6e 7320 776f 726b ... options work\n+00003440: 206a 7573 7420 6669 6e65 2069 6e20 e280 just fine in ..\n+00003450: 9873 6b65 7463 68e2 8099 2e20 2049 660a .sketch.... If.\n+00003460: 6765 6e65 7261 7469 6e67 20e2 8098 5053 generating ...PS\n+00003470: 5472 6963 6b73 e280 992c 2074 6865 2063 Tricks..., the c\n+00003480: 6f64 650a 2020 706f 6c79 676f 6e5b 6669 ode. polygon[fi\n+00003490: 6c6c 636f 6c6f 723d 6c69 6768 7467 7261 llcolor=lightgra\n+000034a0: 792c 6c69 6e65 7769 6474 683d 3370 745d y,linewidth=3pt]\n+000034b0: 2830 2c30 2c31 2928 312c 302c 3029 2830 (0,0,1)(1,0,0)(0\n+000034c0: 2c31 2c30 290a 2020 6c69 6e65 5b6c 696e ,1,0). line[lin\n+000034d0: 6573 7479 6c65 3d64 6f74 7465 645d 282d estyle=dotted](-\n+000034e0: 312c 2d31 2c2d 3129 2832 2c32 2c32 290a 1,-1,-1)(2,2,2).\n+000034f0: 7072 6f64 7563 6573 0a0a 0008 5b69 6d61 produces....[ima\n+00003500: 6765 2073 7263 3d22 6578 3033 302e 706e ge src=\"ex030.pn\n+00003510: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+00003520: 7830 3330 206f 6d69 7474 6564 2069 6e20 x030 omitted in \n+00003530: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+00003540: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+00003550: 085d 0a0a 2020 2054 6f20 7072 6f64 7563 .].. To produc\n+00003560: 6520 e280 9854 696b 5a2f 5047 46e2 8099 e ...TikZ/PGF...\n+00003570: 2c20 7468 6520 636f 7272 6573 706f 6e64 , the correspond\n+00003580: 696e 6720 636f 6465 2069 730a 2020 706f ing code is. po\n+00003590: 6c79 676f 6e5b 6669 6c6c 3d6c 6967 6874 lygon[fill=light\n+000035a0: 6772 6179 2c6c 696e 6520 7769 6474 683d gray,line width=\n+000035b0: 3370 745d 2830 2c30 2c31 2928 312c 302c 3pt](0,0,1)(1,0,\n+000035c0: 3029 2830 2c31 2c30 290a 2020 6c69 6e65 0)(0,1,0). line\n+000035d0: 5b73 7479 6c65 3d64 6f74 7465 645d 282d [style=dotted](-\n+000035e0: 312c 2d31 2c2d 3129 2832 2c32 2c32 290a 1,-1,-1)(2,2,2).\n+000035f0: 2020 676c 6f62 616c 207b 206c 616e 6775 global { langu\n+00003600: 6167 6520 7469 6b7a 207d 0a54 6865 2066 age tikz }.The f\n+00003610: 696e 616c 20e2 8098 676c 6f62 616c e280 inal ...global..\n+00003620: 9920 696e 7374 7275 6374 7320 e280 9873 . instructs ...s\n+00003630: 6b65 7463 68e2 8099 2074 6f20 7072 6f64 ketch... to prod\n+00003640: 7563 6520 e280 9854 696b 5a2f 5047 46e2 uce ...TikZ/PGF.\n+00003650: 8099 2063 6f64 6520 6173 0a6f 7574 7075 .. code as.outpu\n+00003660: 7420 7261 7468 6572 2074 6861 6e20 7468 t rather than th\n+00003670: 6520 6465 6661 756c 742c 20e2 8098 5053 e default, ...PS\n+00003680: 5472 6963 6b73 e280 992e 2020 4e6f 7465 Tricks.... Note\n+00003690: 2074 6861 7420 e280 9870 6f6c 7967 6f6e that ...polygon\n+000036a0: e280 9920 6669 6c6c 0a63 6f6c 6f72 2061 ... fill.color a\n+000036b0: 6e64 20e2 8098 6c69 6e65 e280 9920 7374 nd ...line... st\n+000036c0: 796c 6520 6f70 7469 6f6e 7320 626f 7468 yle options both\n+000036d0: 2063 6f6e 666f 726d 2074 6f20 e280 9854 conform to ...T\n+000036e0: 696b 5ae2 8099 2073 796e 7461 7820 7275 ikZ... syntax ru\n+000036f0: 6c65 732e 2020 5468 650a 7265 7375 6c74 les. The.result\n+00003700: 696e 6720 e280 9854 696b 5a2f 5047 46e2 ing ...TikZ/PGF.\n+00003710: 8099 206f 7574 7075 7420 6973 0a20 205c .. output is. \\\n+00003720: 6265 6769 6e7b 7469 6b7a 7069 6374 7572 begin{tikzpictur\n+00003730: 657d 5b6a 6f69 6e3d 726f 756e 645d 0a20 e}[join=round]. \n+00003740: 205c 6472 6177 5b64 6f74 7465 645d 282d \\draw[dotted](-\n+00003750: 312c 2d31 292d 2d28 2e33 3333 2c2e 3333 1,-1)--(.333,.33\n+00003760: 3329 3b0a 2020 5c66 696c 6c64 7261 775b 3);. \\filldraw[\n+00003770: 6669 6c6c 3d6c 6967 6874 6772 6179 2c6c fill=lightgray,l\n+00003780: 696e 6520 7769 6474 683d 3370 745d 2830 ine width=3pt](0\n+00003790: 2c30 292d 2d28 312c 3029 2d2d 2830 2c31 ,0)--(1,0)--(0,1\n+000037a0: 292d 2d63 7963 6c65 3b0a 2020 5c64 7261 )--cycle;. \\dra\n+000037b0: 775b 646f 7474 6564 5d28 2e33 3333 2c2e w[dotted](.333,.\n+000037c0: 3333 3329 2d2d 2832 2c32 293b 0a20 205c 333)--(2,2);. \\\n+000037d0: 656e 647b 7469 6b7a 7069 6374 7572 657d end{tikzpicture}\n+000037e0: 0a54 6865 2072 656d 6169 6e69 6e67 2065 .The remaining e\n+000037f0: 7861 6d70 6c65 7320 6f66 2074 6869 7320 xamples of this \n+00003800: 6d61 6e75 616c 2061 7265 2069 6e20 5053 manual are in PS\n+00003810: 5472 6963 6b73 2073 7479 6c65 2e0a 0a1f Tricks style....\n+00003820: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00003830: 666f 2c20 204e 6f64 653a 2044 7261 7769 fo, Node: Drawi\n+00003840: 6e67 2061 2073 6f6c 6964 2c20 204e 6578 ng a solid, Nex\n+00003850: 743a 2053 7065 6369 616c 206f 626a 6563 t: Special objec\n+00003860: 7473 2c20 2050 7265 763a 2044 7261 7769 ts, Prev: Drawi\n+00003870: 6e67 206f 7074 696f 6e73 2c20 2055 703a ng options, Up:\n+00003880: 2049 6e74 726f 6475 6374 696f 6e20 6279 Introduction by\n+00003890: 2065 7861 6d70 6c65 0a0a 322e 3320 4472 example..2.3 Dr\n+000038a0: 6177 696e 6720 6120 736f 6c69 640a 3d3d awing a solid.==\n 000038b0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-000038c0: 3d3d 3d0a 0a4c 6574 2773 2074 7279 2073 ===..Let's try s\n-000038d0: 6f6d 6574 6869 6e67 206d 6f72 6520 6578 omething more ex\n-000038e0: 6369 7469 6e67 2e20 20e2 8098 536b 6574 citing. ...Sket\n-000038f0: 6368 e280 9920 6861 7320 6e6f 206e 6f74 ch... has no not\n-00003900: 696f 6e20 6f66 2061 2073 6f6c 6964 2c0a ion of a solid,.\n-00003910: 6275 7420 706f 6c79 676f 6e61 6c20 e280 but polygonal ..\n-00003920: 9c66 6163 6573 e280 9d20 6361 6e20 6265 .faces... can be\n-00003930: 2075 7365 6420 746f 2072 6570 7265 7365 used to represe\n-00003940: 6e74 2074 6865 2062 6f75 6e64 6172 7920 nt the boundary \n-00003950: 6f66 2061 2073 6f6c 6964 2e0a 546f 2074 of a solid..To t\n-00003960: 6865 2070 7265 7669 6f75 7320 6578 616d he previous exam\n-00003970: 706c 652c 206c 6574 2773 2061 6464 2074 ple, let's add t\n-00003980: 6872 6565 206d 6f72 6520 7472 6961 6e67 hree more triang\n-00003990: 756c 6172 2070 6f6c 7967 6f6e 7320 746f ular polygons to\n-000039a0: 0a6d 616b 6520 7468 6520 6661 6365 7320 .make the faces \n-000039b0: 6f66 2061 6e20 6972 7265 6775 6c61 7220 of an irregular \n-000039c0: 7465 7472 6168 6564 726f 6e2e 0a20 2025 tetrahedron.. %\n-000039d0: 2076 6572 7469 6365 7320 6f66 2074 6865 vertices of the\n-000039e0: 2074 6574 7261 6865 6472 6f6e 0a20 2064 tetrahedron. d\n-000039f0: 6566 2070 3120 2830 2c30 2c31 2920 6465 ef p1 (0,0,1) de\n-00003a00: 6620 7032 2028 312c 302c 3029 0a20 2064 f p2 (1,0,0). d\n-00003a10: 6566 2070 3320 2830 2c31 2c30 2920 6465 ef p3 (0,1,0) de\n-00003a20: 6620 7034 2028 2d2e 332c 2d2e 352c 2d2e f p4 (-.3,-.5,-.\n-00003a30: 3829 0a0a 2020 2520 6661 6365 7320 6f66 8).. % faces of\n-00003a40: 2074 6865 2074 6574 7261 6865 6472 6f6e the tetrahedron\n-00003a50: 2e0a 2020 706f 6c79 676f 6e28 7031 2928 .. polygon(p1)(\n-00003a60: 7032 2928 7033 2920 2520 6f72 6967 696e p2)(p3) % origin\n-00003a70: 616c 2066 726f 6e74 2070 6f6c 7967 6f6e al front polygon\n-00003a80: 0a20 2070 6f6c 7967 6f6e 2870 3129 2870 . polygon(p1)(p\n-00003a90: 3429 2870 3229 2025 2062 6f74 746f 6d0a 4)(p2) % bottom.\n-00003aa0: 2020 706f 6c79 676f 6e28 7031 2928 7033 polygon(p1)(p3\n-00003ab0: 2928 7034 2920 2520 6c65 6674 0a20 2070 )(p4) % left. p\n-00003ac0: 6f6c 7967 6f6e 2870 3329 2870 3229 2870 olygon(p3)(p2)(p\n-00003ad0: 3429 2025 2072 6561 720a 0a20 2025 206c 4) % rear.. % l\n-00003ae0: 696e 6520 746f 2070 6965 7263 6520 7468 ine to pierce th\n-00003af0: 6520 7465 7472 6168 6564 726f 6e0a 2020 e tetrahedron. \n-00003b00: 6c69 6e65 5b6c 696e 6563 6f6c 6f72 3d72 line[linecolor=r\n-00003b10: 6564 5d28 2d31 2c2d 312c 2d31 2928 322c ed](-1,-1,-1)(2,\n-00003b20: 322c 3229 0a54 6869 7320 6578 616d 706c 2,2).This exampl\n-00003b30: 6520 7573 6573 20e2 809c 6465 6669 6e69 e uses ...defini\n-00003b40: 7469 6f6e 73e2 809d 2c20 7768 6963 6820 tions..., which \n-00003b50: 6265 6769 6e20 7769 7468 20e2 8098 6465 begin with ...de\n-00003b60: 66e2 8099 2e20 2054 6865 7365 20e2 809c f.... These ...\n-00003b70: 6465 6669 6e65 e280 9d0a 6f72 2067 6976 define....or giv\n-00003b80: 6520 6e61 6d65 7320 746f 2070 6f69 6e74 e names to point\n-00003b90: 732c 2077 6869 6368 2061 7265 2074 6865 s, which are the\n-00003ba0: 6e20 6176 6169 6c61 626c 6520 6173 20e2 n available as .\n-00003bb0: 809c 7265 6665 7265 6e63 6573 e280 9d20 ..references... \n-00003bc0: 6279 0a65 6e63 6c6f 7369 6e67 2074 6865 by.enclosing the\n-00003bd0: 206e 616d 6573 2069 6e20 7061 7265 6e74 names in parent\n-00003be0: 6865 7365 732c 2065 2e67 2e20 2866 6f6f heses, e.g. (foo\n-00003bf0: 292e 2020 5468 6520 7061 7265 6e74 6865 ). The parenthe\n-00003c00: 7365 7320 6465 6e6f 7465 0a74 6861 7420 ses denote.that \n-00003c10: 7468 6520 6e61 6d65 7320 7265 6665 7220 the names refer \n-00003c20: 746f 2070 6f69 6e74 733b 2074 6865 7920 to points; they \n-00003c30: 6172 6520 7265 7175 6972 6564 2e20 2054 are required. T\n-00003c40: 6865 7265 2063 616e 2062 6520 6e6f 0a77 here can be no.w\n-00003c50: 6869 7465 2073 7061 6365 2062 6574 7765 hite space betwe\n-00003c60: 656e 2074 6865 6d20 616e 6420 7468 6520 en them and the \n-00003c70: 6e61 6d65 2e0a 0a20 2020 4173 2079 6f75 name... As you\n-00003c80: 2063 616e 2073 6565 2c20 636f 6d6d 656e can see, commen\n-00003c90: 7473 2073 7461 7274 2077 6974 6820 2520 ts start with % \n-00003ca0: 6173 2069 6e20 5465 5820 616e 6420 6578 as in TeX and ex\n-00003cb0: 7465 6e64 2074 6f20 7468 6520 656e 640a tend to the end.\n-00003cc0: 6f66 2074 6865 206c 696e 6520 2874 686f of the line (tho\n-00003cd0: 7567 6820 2320 7769 6c6c 2077 6f72 6b20 ugh # will work \n-00003ce0: 6173 2077 656c 6c29 2e20 2057 6869 7465 as well). White\n-00003cf0: 2073 7061 6365 2c20 696e 636c 7564 696e space, includin\n-00003d00: 670a 7370 6163 6573 2c20 7461 6273 2061 g.spaces, tabs a\n-00003d10: 6e64 2062 6c61 6e6b 206c 696e 6573 2c20 nd blank lines, \n-00003d20: 6861 7320 6e6f 2065 6666 6563 7420 696e has no effect in\n-00003d30: 2074 6865 20e2 8098 736b 6574 6368 e280 the ...sketch..\n-00003d40: 9920 6c61 6e67 7561 6765 2e0a 0a00 085b . language.....[\n-00003d50: 696d 6167 6520 7372 633d 2265 7830 3430 image src=\"ex040\n-00003d60: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n-00003d70: 6520 6578 3034 3020 6f6d 6974 7465 6420 e ex040 omitted \n-00003d80: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n-00003d90: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n-00003da0: 2e22 0008 5d0a 0a49 6620 7765 206c 6f6f .\"..]..If we loo\n-00003db0: 6b20 696e 7369 6465 2074 6865 2054 6558 k inside the TeX\n-00003dc0: 2066 696c 6520 7072 6f64 7563 6564 2062 file produced b\n-00003dd0: 7920 e280 9873 6b65 7463 68e2 8099 2c20 y ...sketch..., \n-00003de0: 7468 6572 6520 7769 6c6c 2062 6520 6f6e there will be on\n-00003df0: 6c79 0a74 6872 6565 2070 6f6c 7967 6f6e ly.three polygon\n-00003e00: 732e 2020 5468 6520 666f 7572 7468 2068 s. The fourth h\n-00003e10: 6173 2062 6565 6e20 6375 6c6c 6564 2062 as been culled b\n-00003e20: 6563 6175 7365 2069 7420 6973 2061 2022 ecause it is a \"\n-00003e30: 6261 636b 2066 6163 6522 0a6f 6620 7468 back face\".of th\n-00003e40: 6520 7465 7472 6168 6564 726f 6e2c 2069 e tetrahedron, i\n-00003e50: 6e76 6973 6962 6c65 2074 6f20 6f75 7220 nvisible to our \n-00003e60: 7669 6577 2e20 2049 7420 6973 2075 6e6e view. It is unn\n-00003e70: 6563 6573 7361 7279 2c20 616e 6420 736f ecessary, and so\n-00003e80: 2069 740a 6973 2072 656d 6f76 6564 2e0a it.is removed..\n-00003e90: 0a20 2020 496e 2073 6f6d 6520 6472 6177 . In some draw\n-00003ea0: 696e 6773 2c20 706f 6c79 676f 6e73 2061 ings, polygons a\n-00003eb0: 6374 2061 7320 7a65 726f 2d74 6869 636b ct as zero-thick\n-00003ec0: 6e65 7373 2073 6f6c 6964 2073 7572 6661 ness solid surfa\n-00003ed0: 6365 7320 7769 7468 0a62 6f74 6820 7369 ces with.both si\n-00003ee0: 6465 7320 7669 7369 626c 6520 7261 7468 des visible rath\n-00003ef0: 6572 2074 6861 6e20 6173 2074 6865 2066 er than as the f\n-00003f00: 6163 6573 206f 6620 736f 6c69 6420 6f62 aces of solid ob\n-00003f10: 6a65 6374 732c 2077 6865 7265 2062 6163 jects, where bac\n-00003f20: 6b0a 6661 6365 7320 6361 6e20 6265 2063 k.faces can be c\n-00003f30: 756c 6c65 642e 2020 466f 7220 7a65 726f ulled. For zero\n-00003f40: 2d74 6869 636b 6e65 7373 2073 6f6c 6964 -thickness solid\n-00003f50: 732c 2063 756c 6c69 6e67 2069 7320 6120 s, culling is a \n-00003f60: 7072 6f62 6c65 6d2e 0a4f 6e65 2073 6f6c problem..One sol\n-00003f70: 7574 696f 6e20 6973 2074 6f20 7573 6520 ution is to use \n-00003f80: 6120 7061 6972 206f 6620 e280 9873 6b65 a pair of ...ske\n-00003f90: 7463 68e2 8099 2070 6f6c 7967 6f6e 7320 tch... polygons \n-00003fa0: 666f 7220 6561 6368 0a7a 6572 6f2d 7468 for each.zero-th\n-00003fb0: 6963 6b6e 6573 7320 6661 6365 2c20 6964 ickness face, id\n-00003fc0: 656e 7469 6361 6c20 6578 6365 7074 2077 entical except w\n-00003fd0: 6974 6820 6f70 706f 7369 7465 2076 6572 ith opposite ver\n-00003fe0: 7465 7820 6f72 6465 7273 2e20 2054 6869 tex orders. Thi\n-00003ff0: 730a 6973 2075 6e77 6965 6c64 7920 616e s.is unwieldy an\n-00004000: 6420 6578 7065 6e73 6976 652e 2020 4120 d expensive. A \n-00004010: 6265 7474 6572 2077 6179 2069 7320 746f better way is to\n-00004020: 2073 6574 2074 6865 20e2 8098 736b 6574 set the ...sket\n-00004030: 6368 e280 9920 696e 7465 726e 616c 0a6f ch... internal.o\n-00004040: 7074 696f 6e20 e280 9863 756c 6ce2 8099 ption ...cull...\n-00004050: 2074 6f20 e280 9866 616c 7365 e280 9920 to ...false... \n-00004060: 696e 2074 6865 2075 7375 616c 20e2 8098 in the usual ...\n-00004070: 5053 5472 6963 6b73 e280 9920 6d61 6e6e PSTricks... mann\n-00004080: 6572 2e0a 2020 706f 6c79 676f 6e5b 6375 er.. polygon[cu\n-00004090: 6c6c 3d66 616c 7365 5d28 7031 2928 7032 ll=false](p1)(p2\n-000040a0: 2928 7033 290a 5468 6520 666f 6c6c 6f77 )(p3).The follow\n-000040b0: 696e 6720 7368 6f77 7320 7468 6520 7361 ing shows the sa\n-000040c0: 6d65 2068 656c 6978 2073 6861 7065 2064 me helix shape d\n-000040d0: 7261 776e 2066 6972 7374 2077 6974 6820 rawn first with \n-000040e0: 6375 6c6c 3d74 7275 6520 2874 6865 0a64 cull=true (the.d\n-000040f0: 6566 6175 6c74 2920 616e 6420 7468 656e efault) and then\n-00004100: 2063 756c 6c3d 6661 6c73 652e 0a0a 0008 cull=false.....\n-00004110: 5b69 6d61 6765 2073 7263 3d22 6578 3034 [image src=\"ex04\n-00004120: 352e 706e 6722 2074 6578 743d 2249 6d61 5.png\" text=\"Ima\n-00004130: 6765 2065 7830 3435 206f 6d69 7474 6564 ge ex045 omitted\n-00004140: 2069 6e20 7465 7874 2076 6572 7369 6f6e in text version\n-00004150: 206f 6620 7468 6973 2064 6f63 756d 656e of this documen\n-00004160: 742e 2200 085d 0a0a 5765 276c 6c20 736f t.\"..]..We'll so\n-00004170: 6f6e 2073 6565 2068 6f77 2074 6f20 7072 on see how to pr\n-00004180: 6f64 7563 6520 7468 6573 6520 6865 6c69 oduce these heli\n-00004190: 7865 7320 7769 7468 2061 2066 6577 206c xes with a few l\n-000041a0: 696e 6573 206f 6620 e280 9873 6b65 7463 ines of ...sketc\n-000041b0: 68e2 8099 0a6c 616e 6775 6167 6520 636f h....language co\n-000041c0: 6465 2e0a 0a20 2020 4974 206d 6179 2062 de... It may b\n-000041d0: 6520 7465 6d70 7469 6e67 2074 6f20 7475 e tempting to tu\n-000041e0: 726e 2063 756c 6c69 6e67 206f 6666 2067 rn culling off g\n-000041f0: 7261 7475 6974 6f75 736c 7920 736f 2074 ratuitously so t\n-00004200: 6861 7420 7665 7274 6578 0a6f 7264 6572 hat vertex.order\n-00004210: 2063 616e 2062 6520 6967 6e6f 7265 642e can be ignored.\n-00004220: 2020 5468 6973 2069 7320 6e6f 7420 6120 This is not a \n-00004230: 676f 6f64 2069 6465 6120 6265 6361 7573 good idea becaus\n-00004240: 6520 6f75 7470 7574 2066 696c 6520 7369 e output file si\n-00004250: 7a65 0a61 6e64 2054 6558 2061 6e64 2050 ze.and TeX and P\n-00004260: 6f73 7473 6372 6970 7420 7072 6f63 6573 ostscript proces\n-00004270: 7369 6e67 2074 696d 6520 626f 7468 2064 sing time both d\n-00004280: 6570 656e 6420 6f6e 2074 6865 206e 756d epend on the num\n-00004290: 6265 7220 6f66 0a6f 7574 7075 7420 706f ber of.output po\n-000042a0: 6c79 676f 6e73 2e20 2043 756c 6c69 6e67 lygons. Culling\n-000042b0: 2075 7375 616c 6c79 2069 6d70 726f 7665 usually improve\n-000042c0: 7320 7065 7266 6f72 6d61 6e63 6520 6279 s performance by\n-000042d0: 2061 2066 6163 746f 7220 6f66 0a74 776f a factor of.two\n-000042e0: 2e20 204f 6e20 7468 6520 6f74 6865 7220 . On the other \n-000042f0: 6861 6e64 2c20 676c 6f62 616c 6c79 2073 hand, globally s\n-00004300: 6574 7469 6e67 20e2 8098 6375 6c6c 3d66 etting ...cull=f\n-00004310: 616c 7365 e280 9920 6973 2072 6561 736f alse... is reaso\n-00004320: 6e61 626c 650a 7768 696c 6520 6465 6275 nable.while debu\n-00004330: 6767 696e 672e 2020 5365 6520 2a6e 6f74 gging. See *not\n-00004340: 6520 476c 6f62 616c 206f 7074 696f 6e73 e Global options\n-00004350: 3a3a 2061 6e64 202a 6e6f 7465 204c 696d :: and *note Lim\n-00004360: 6974 7320 6f6e 2065 7272 6f72 0a64 6574 its on error.det\n-00004370: 6563 7469 6f6e 3a3a 2e0a 0a1f 0a46 696c ection::.....Fil\n-00004380: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-00004390: 204e 6f64 653a 2053 7065 6369 616c 206f Node: Special o\n-000043a0: 626a 6563 7473 2c20 204e 6578 743a 204f bjects, Next: O\n-000043b0: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n-000043c0: 2c20 2050 7265 763a 2044 7261 7769 6e67 , Prev: Drawing\n-000043d0: 2061 2073 6f6c 6964 2c20 2055 703a 2049 a solid, Up: I\n-000043e0: 6e74 726f 6475 6374 696f 6e20 6279 2065 ntroduction by e\n-000043f0: 7861 6d70 6c65 0a0a 322e 3420 5370 6563 xample..2.4 Spec\n-00004400: 6961 6c20 6f62 6a65 6374 730a 3d3d 3d3d ial objects.====\n-00004410: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a ===============.\n-00004420: 0a57 6520 6361 6e20 6164 6420 6c61 6265 .We can add labe\n-00004430: 6c73 2074 6f20 6120 6472 6177 696e 6720 ls to a drawing \n-00004440: 6279 2075 7369 6e67 2073 7065 6369 616c by using special\n-00004450: 206f 626a 6563 7473 2c20 7768 6963 6820 objects, which \n-00004460: 7072 6f76 6964 6520 610a 7761 7920 746f provide a.way to\n-00004470: 2065 6d62 6564 2072 6177 204c 6154 6558 embed raw LaTeX\n-00004480: 2061 6e64 20e2 8098 5053 5472 6963 6b73 and ...PSTricks\n-00004490: e280 9920 636f 6465 2e20 2041 6464 696e ... code. Addin\n-000044a0: 6720 7468 6973 2074 6f20 7468 650a 7465 g this to the.te\n-000044b0: 7472 6168 6564 726f 6e20 646f 6573 2074 trahedron does t\n-000044c0: 6865 2074 7269 636b 2e0a 2020 7370 6563 he trick.. spec\n-000044d0: 6961 6c20 7c5c 666f 6f74 6e6f 7465 7369 ial |\\footnotesi\n-000044e0: 7a65 0a20 2020 2020 2020 2020 2020 5c75 ze. \\u\n-000044f0: 7075 747b 3270 747d 5b75 725d 2331 7b24 put{2pt}[ur]#1{$\n-00004500: 5031 247d 0a20 2020 2020 2020 2020 2020 P1$}. \n-00004510: 5c75 7075 745b 725d 2332 7b24 5032 247d \\uput[r]#2{$P2$}\n-00004520: 0a20 2020 2020 2020 2020 2020 5c75 7075 . \\upu\n-00004530: 745b 755d 2333 7b24 5033 247d 0a20 2020 t[u]#3{$P3$}. \n-00004540: 2020 2020 2020 2020 5c75 7075 745b 645d \\uput[d]\n-00004550: 2334 7b24 5034 247d 7c0a 2020 2020 2870 #4{$P4$}|. (p\n-00004560: 3129 2870 3229 2870 3329 2870 3429 0a48 1)(p2)(p3)(p4).H\n-00004570: 6572 6520 6973 2074 6865 2072 6573 756c ere is the resul\n-00004580: 742e 0a0a 0008 5b69 6d61 6765 2073 7263 t.....[image src\n-00004590: 3d22 6578 3034 322e 706e 6722 2074 6578 =\"ex042.png\" tex\n-000045a0: 743d 2249 6d61 6765 2065 7830 3432 206f t=\"Image ex042 o\n-000045b0: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n-000045c0: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n-000045d0: 6f63 756d 656e 742e 2200 085d 0a0a 2020 ocument.\"..].. \n-000045e0: 2054 6865 7265 2061 7265 2073 6576 6572 There are sever\n-000045f0: 616c 2064 6574 6169 6c73 2074 6f20 6e6f al details to no\n-00004600: 7465 2068 6572 652e 2020 4669 7273 742c te here. First,\n-00004610: 2074 6865 2071 756f 7469 6e67 0a63 6f6e the quoting.con\n-00004620: 7665 6e74 696f 6e20 666f 7220 7468 6520 vention for the \n-00004630: 7261 7720 636f 6465 2069 7320 7369 6d69 raw code is simi\n-00004640: 6c61 7220 746f 2074 6865 204c 6154 6558 lar to the LaTeX\n-00004650: 205c 7665 7262 2063 6f6d 6d61 6e64 2e20 \\verb command. \n-00004660: 2054 6865 0a66 6972 7374 206e 6f6e 2d77 The.first non-w\n-00004670: 6869 7465 2073 7061 6365 2063 6861 7261 hite space chara\n-00004680: 6374 6572 2066 6f6c 6c6f 7769 6e67 2073 cter following s\n-00004690: 7065 6369 616c 2069 7320 756e 6465 7273 pecial is unders\n-000046a0: 746f 6f64 2074 6f20 6265 0a74 6865 2071 tood to be.the q\n-000046b0: 756f 7465 2063 6861 7261 6374 6572 2c20 uote character, \n-000046c0: 696e 2074 6869 7320 6361 7365 20e2 8098 in this case ...\n-000046d0: 7ce2 8099 2e20 2054 6865 2072 6177 2074 |.... The raw t\n-000046e0: 6578 7420 636f 6e74 696e 7565 7320 756e ext continues un\n-000046f0: 7469 6c0a 7468 6973 2063 6861 7261 6374 til.this charact\n-00004700: 6572 2072 6563 7572 732e 0a0a 2020 2053 er recurs... S\n-00004710: 6563 6f6e 642c 2074 6865 2061 7267 756d econd, the argum\n-00004720: 656e 7420 7265 6665 7265 6e63 6573 2023 ent references #\n-00004730: 312c 2023 322c 2023 332c 2061 6e64 2023 1, #2, #3, and #\n-00004740: 3420 7265 6665 7220 746f 2070 6f69 6e74 4 refer to point\n-00004750: 2c0a 7665 6374 6f72 2c20 6f72 2073 6361 ,.vector, or sca\n-00004760: 6c61 7220 7661 6c75 6573 2069 6e20 7468 lar values in th\n-00004770: 6520 6c69 7374 2074 6861 7420 666f 6c6c e list that foll\n-00004780: 6f77 2e20 2054 6869 7320 6973 2073 696d ow. This is sim\n-00004790: 696c 6172 2074 6f0a 5465 5820 6d61 6372 ilar to.TeX macr\n-000047a0: 6f20 7379 6e74 6178 2e20 2054 6865 2074 o syntax. The t\n-000047b0: 7261 6e73 666f 726d 6564 2061 6e64 2074 ransformed and t\n-000047c0: 776f 2d64 696d 656e 7369 6f6e 616c 2070 wo-dimensional p\n-000047d0: 726f 6a65 6374 696f 6e73 206f 660a 7468 rojections of.th\n-000047e0: 6573 6520 7468 7265 652d 6469 6d65 6e73 ese three-dimens\n-000047f0: 696f 6e61 6c20 706f 696e 7473 2061 7265 ional points are\n-00004800: 2073 7562 7374 6974 7574 6564 2069 6e20 substituted in \n-00004810: 7468 6520 6669 6e61 6c20 6f75 7470 7574 the final output\n-00004820: 2e20 2041 6e0a 6172 6775 6d65 6e74 2072 . An.argument r\n-00004830: 6566 6572 656e 6365 206f 6620 7468 6520 eference of the \n-00004840: 666f 726d 2023 312d 3220 6973 2072 6570 form #1-2 is rep\n-00004850: 6c61 6365 6420 7769 7468 2074 6865 2061 laced with the a\n-00004860: 6e67 6c65 2069 6e0a 6465 6772 6565 7320 ngle in.degrees \n-00004870: 6f66 2074 6865 2074 776f 2d64 696d 656e of the two-dimen\n-00004880: 7369 6f6e 616c 2076 6563 746f 7220 7468 sional vector th\n-00004890: 6174 2063 6f6e 6e65 6374 7320 7468 6520 at connects the \n-000048a0: 7072 6f6a 6563 7469 6f6e 7320 6f66 0a74 projections of.t\n-000048b0: 6865 2074 776f 2072 6573 7065 6374 6976 he two respectiv\n-000048c0: 6520 6172 6775 6d65 6e74 2070 6f69 6e74 e argument point\n-000048d0: 732c 2068 6572 6520 2331 2061 6e64 2023 s, here #1 and #\n-000048e0: 322e 2020 5468 6520 7375 6273 7469 7475 2. The substitu\n-000048f0: 7465 640a 616e 676c 6520 6973 2065 6e63 ted.angle is enc\n-00004900: 6c6f 7365 6420 696e 2063 7572 6c79 2062 losed in curly b\n-00004910: 7261 6365 7320 e280 987b 207d e280 992e races ...{ }....\n-00004920: 2020 5768 656e 20e2 8098 5469 6b5a 2f50 When ...TikZ/P\n-00004930: 4746 e280 9920 6f75 7470 7574 2069 730a GF... output is.\n-00004940: 6265 696e 6720 6765 6e65 7261 7465 642c being generated,\n-00004950: 2074 6865 2061 6e67 6c65 2069 7320 726f the angle is ro\n-00004960: 756e 6465 6420 746f 2074 6865 206e 6561 unded to the nea\n-00004970: 7265 7374 2064 6567 7265 6520 6265 6361 rest degree beca\n-00004980: 7573 650a 6e6f 6e2d 696e 7465 6765 7220 use.non-integer \n-00004990: 616e 676c 6573 2061 7265 206e 6f74 2061 angles are not a\n-000049a0: 6c6c 6f77 6564 2062 7920 e280 9854 696b llowed by ...Tik\n-000049b0: 5a2f 5047 46e2 8099 2070 7269 6d69 7469 Z/PGF... primiti\n-000049c0: 7665 732e 0a0a 2020 2041 7320 6f66 2056 ves... As of V\n-000049d0: 6572 7369 6f6e 2030 2e33 206f 6620 e280 ersion 0.3 of ..\n-000049e0: 9873 6b65 7463 68e2 8099 2c20 7370 6563 .sketch..., spec\n-000049f0: 6961 6c20 6172 6775 6d65 6e74 7320 6d61 ial arguments ma\n-00004a00: 7920 6265 2073 6361 6c61 7273 206f 720a y be scalars or.\n-00004a10: 7665 6374 6f72 7320 696e 2061 6464 6974 vectors in addit\n-00004a20: 696f 6e20 746f 2070 6f69 6e74 732e 2020 ion to points. \n-00004a30: 5265 6665 7265 6e63 6573 2074 6f20 7363 References to sc\n-00004a40: 616c 6172 2061 7267 756d 656e 7473 2061 alar arguments a\n-00004a50: 7265 0a6d 6572 656c 7920 7265 706c 6163 re.merely replac\n-00004a60: 6564 2077 6974 6820 6120 6e75 6d62 6572 ed with a number\n-00004a70: 2066 6f72 6d61 7474 6564 206a 7573 7420 formatted just \n-00004a80: 6173 2061 6e79 2070 6f69 6e74 2063 6f6f as any point coo\n-00004a90: 7264 696e 6174 652e 0a52 6566 6572 656e rdinate..Referen\n-00004aa0: 6365 7320 746f 2076 6563 746f 7273 2062 ces to vectors b\n-00004ab0: 6563 6f6d 6520 7477 6f2d 6469 6d65 6e73 ecome two-dimens\n-00004ac0: 696f 6e61 6c20 706f 696e 7473 2e20 2054 ional points. T\n-00004ad0: 6865 2074 6963 6b20 6f70 6572 6174 6f72 he tick operator\n-00004ae0: 0a74 6861 7420 7365 6c65 6374 7320 696e .that selects in\n-00004af0: 6469 7669 6475 616c 2063 6f6d 706f 6e65 dividual compone\n-00004b00: 6e74 7320 6f66 2070 6f69 6e74 7320 616e nts of points an\n-00004b10: 6420 7665 6374 6f72 7320 656c 7365 7768 d vectors elsewh\n-00004b20: 6572 6520 696e 0ae2 8098 736b 6574 6368 ere in....sketch\n-00004b30: e280 9920 2873 6565 2066 6f72 2065 7861 ... (see for exa\n-00004b40: 6d70 6c65 202a 6e6f 7465 2041 6666 696e mple *note Affin\n-00004b50: 6520 6172 6974 686d 6574 6963 3a3a 2920 e arithmetic::) \n-00004b60: 6361 6e20 616c 736f 2062 6520 6170 706c can also be appl\n-00004b70: 6965 640a 746f 2070 6f69 6e74 2061 6e64 ied.to point and\n-00004b80: 2076 6563 746f 7220 6172 6775 6d65 6e74 vector argument\n-00004b90: 2072 6566 6572 656e 6365 732e 2020 416c references. Al\n-00004ba0: 6c20 7468 7265 6520 6469 6d65 6e73 696f l three dimensio\n-00004bb0: 6e73 206f 6620 610a 7472 616e 7366 6f72 ns of a.transfor\n-00004bc0: 6d65 6420 706f 696e 7420 6f72 2076 6563 med point or vec\n-00004bd0: 746f 7220 6361 6e20 616c 736f 2062 6520 tor can also be \n-00004be0: 7375 6273 7469 7475 6564 2077 6974 6820 substitued with \n-00004bf0: e280 9827 33e2 8099 2e20 2053 6565 202a ...'3.... See *\n-00004c00: 6e6f 7465 0a53 7065 6369 616c 733a 3a20 note.Specials:: \n-00004c10: 666f 7220 6465 7461 696c 732e 0a0a 2020 for details... \n-00004c20: 2042 7920 6465 6661 756c 742c 20e2 8098 By default, ...\n-00004c30: 7370 6563 6961 6ce2 8099 206f 626a 6563 special... objec\n-00004c40: 7473 2061 7265 2070 7269 6e74 6564 206c ts are printed l\n-00004c50: 6173 742c 206f 7665 726c 6179 696e 6720 ast, overlaying \n-00004c60: 616c 6c20 6f74 6865 720a 6f62 6a65 6374 all other.object\n-00004c70: 7320 696e 2074 6865 2073 6365 6e65 2e20 s in the scene. \n-00004c80: 2049 6620 796f 7520 7370 6563 6966 7920 If you specify \n-00004c90: 7468 6520 696e 7465 726e 616c 206f 7074 the internal opt\n-00004ca0: 696f 6e20 e280 986c 6179 3d69 6ee2 8099 ion ...lay=in...\n-00004cb0: 2c20 7468 650a 6869 6464 656e 2073 7572 , the.hidden sur\n-00004cc0: 6661 6365 2061 6c67 6f72 6974 686d 2063 face algorithm c\n-00004cd0: 6f6e 7369 6465 7273 2074 6865 2065 6e74 onsiders the ent\n-00004ce0: 6972 6520 7370 6563 6961 6c20 6f62 6a65 ire special obje\n-00004cf0: 6374 2074 6f20 6265 2074 6865 0a66 6972 ct to be the.fir\n-00004d00: 7374 2070 6f69 6e74 2028 2331 2920 696e st point (#1) in\n-00004d10: 2074 6865 2061 7267 756d 656e 7420 6c69 the argument li\n-00004d20: 7374 2e20 2049 6620 7468 6174 2070 6f69 st. If that poi\n-00004d30: 6e74 2069 7320 6265 6869 6e64 2028 6f66 nt is behind (of\n-00004d40: 0a73 6d61 6c6c 6572 207a 2d63 6f6d 706f .smaller z-compo\n-00004d50: 6e65 6e74 2074 6861 6e29 2061 6e79 2064 nent than) any d\n-00004d60: 7261 7761 626c 652c 2074 6865 6e20 7468 rawable, then th\n-00004d70: 6520 656e 7469 7265 2073 7065 6369 616c e entire special\n-00004d80: 206f 626a 6563 740a 6973 2064 7261 776e object.is drawn\n-00004d90: 2062 6566 6f72 6520 7468 6174 2064 7261 before that dra\n-00004da0: 7761 626c 652c 2073 6f20 7468 6520 6472 wable, so the dr\n-00004db0: 6177 6162 6c65 206f 6273 6375 7265 7320 awable obscures \n-00004dc0: 7061 7274 7320 6f66 2074 6865 0a73 7065 parts of the.spe\n-00004dd0: 6369 616c 206f 626a 6563 7420 7468 6174 cial object that\n-00004de0: 206f 7665 726c 6170 7320 6974 2e20 2049 overlaps it. I\n-00004df0: 6e20 6f75 7220 6578 616d 706c 652c 2070 n our example, p\n-00004e00: 3120 6973 2074 6865 2066 726f 6e74 2d6d 1 is the front-m\n-00004e10: 6f73 740a 706f 696e 7420 696e 2074 6865 ost.point in the\n-00004e20: 2073 6365 6e65 2028 6861 7320 7468 6520 scene (has the \n-00004e30: 6c61 7267 6573 7420 7a2d 636f 6d70 6f6e largest z-compon\n-00004e40: 656e 7429 2c20 736f 2061 6464 696e 6720 ent), so adding \n-00004e50: e280 986c 6179 3d69 6ee2 8099 2068 6173 ...lay=in... has\n-00004e60: 0a6e 6f20 6566 6665 6374 2e0a 0a20 2020 .no effect... \n-00004e70: 5769 7468 206f 7074 696f 6e20 e280 986c With option ...l\n-00004e80: 6179 3d75 6e64 6572 e280 992c 2061 2073 ay=under..., a s\n-00004e90: 7065 6369 616c 2069 7320 6472 6177 6e20 pecial is drawn \n-00004ea0: 5f62 6566 6f72 655f 2c20 6865 6e63 6520 _before_, hence \n-00004eb0: 6170 7065 6172 730a 5f75 6e64 6572 5f20 appears._under_ \n-00004ec0: 616e 7920 6f66 2074 6865 206f 626a 6563 any of the objec\n-00004ed0: 7473 2068 616e 646c 6564 2062 7920 7468 ts handled by th\n-00004ee0: 6520 6869 6464 656e 2073 7572 6661 6365 e hidden surface\n-00004ef0: 2061 6c67 6f72 6974 686d 2e0a 5468 6973 algorithm..This\n-00004f00: 2069 7320 686f 7720 7468 6520 6c69 6768 is how the ligh\n-00004f10: 7420 6772 6179 2061 7865 7320 7765 7265 t gray axes were\n-00004f20: 2061 6464 6564 2074 6f20 7468 6520 2268 added to the \"h\n-00004f30: 656c 6c6f 2077 6f72 6c64 2220 6578 616d ello world\" exam\n-00004f40: 706c 650a 2a6e 6f74 6520 4865 6c6c 6f20 ple.*note Hello \n-00004f50: 776f 726c 643a 3a2e 0a0a 2020 2053 7065 world::... Spe\n-00004f60: 6369 616c 206f 626a 6563 7473 2061 7265 cial objects are\n-00004f70: 2070 6f77 6572 6675 6c2c 2077 6974 6820 powerful, with \n-00004f80: 6d61 6e79 2070 6f73 7369 626c 6520 7573 many possible us\n-00004f90: 6573 2e0a 0a1f 0a46 696c 653a 2073 6b65 es.....File: ske\n-00004fa0: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n-00004fb0: 204f 626a 6563 7420 7472 616e 7366 6f72 Object transfor\n-00004fc0: 6d73 2c20 204e 6578 743a 2052 6570 6561 ms, Next: Repea\n-00004fd0: 7465 6420 6f62 6a65 6374 732c 2020 5072 ted objects, Pr\n-00004fe0: 6576 3a20 5370 6563 6961 6c20 6f62 6a65 ev: Special obje\n-00004ff0: 6374 732c 2020 5570 3a20 496e 7472 6f64 cts, Up: Introd\n-00005000: 7563 7469 6f6e 2062 7920 6578 616d 706c uction by exampl\n-00005010: 650a 0a32 2e35 2054 7261 6e73 666f 726d e..2.5 Transform\n-00005020: 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d s.==============\n-00005030: 0a0a 4e6f 7720 6c65 7427 7320 6164 6420 ..Now let's add \n-00005040: 6120 7365 636f 6e64 2063 6f70 7920 6f66 a second copy of\n-00005050: 2074 6865 2070 6965 7263 6564 2074 6574 the pierced tet\n-00005060: 7261 6865 6472 6f6e 2e20 2057 6527 6c6c rahedron. We'll\n-00005070: 2072 6f74 6174 650a 7468 6520 636f 7079 rotate.the copy\n-00005080: 2039 3020 6465 6772 6565 7320 6162 6f75 90 degrees abou\n-00005090: 7420 7468 6520 782d 6178 6973 2077 6974 t the x-axis wit\n-000050a0: 6820 7468 6520 6f72 6967 696e 2061 7320 h the origin as \n-000050b0: e280 9c63 656e 7465 7220 6f66 0a72 6f74 ...center of.rot\n-000050c0: 6174 696f 6ee2 809d 2073 6f20 7765 2063 ation... so we c\n-000050d0: 616e 2073 6565 2074 6865 2062 6163 6b2c an see the back,\n-000050e0: 2074 6865 6e20 7472 616e 736c 6174 6520 then translate \n-000050f0: 6974 2074 6f20 7468 6520 7269 6768 742d it to the right-\n-00005100: 2d69 6e20 7468 650a 706f 7369 7469 7665 -in the.positive\n-00005110: 2078 2d64 6972 6563 7469 6f6e 2d2d 736f x-direction--so\n-00005120: 2069 7420 646f 6573 6e27 7420 636f 6c6c it doesn't coll\n-00005130: 6964 6520 7769 7468 2074 6865 206f 7269 ide with the ori\n-00005140: 6769 6e61 6c2e 2020 546f 2068 656c 700a ginal. To help.\n-00005150: 7573 2073 6565 2077 6861 7427 7320 676f us see what's go\n-00005160: 696e 6720 6f6e 2c20 6d61 6b65 2074 6865 ing on, make the\n-00005170: 2062 6163 6b20 7369 6465 2067 7261 792e back side gray.\n-00005180: 0a20 2064 6566 2070 6965 7263 6564 5f74 . def pierced_t\n-00005190: 6574 7261 6865 6472 6f6e 207b 0a20 2020 etrahedron {. \n-000051a0: 2064 6566 2070 3120 2830 2c30 2c31 2920 def p1 (0,0,1) \n-000051b0: 6465 6620 7032 2028 312c 302c 3029 0a20 def p2 (1,0,0). \n-000051c0: 2020 2064 6566 2070 3320 2830 2c31 2c30 def p3 (0,1,0\n-000051d0: 2920 6465 6620 7034 2028 2d2e 332c 2d2e ) def p4 (-.3,-.\n-000051e0: 352c 2d2e 3829 0a20 2020 2070 6f6c 7967 5,-.8). polyg\n-000051f0: 6f6e 2870 3129 2870 3229 2870 3329 2020 on(p1)(p2)(p3) \n+000038c0: 3d0a 0a4c 6574 2773 2074 7279 2073 6f6d =..Let's try som\n+000038d0: 6574 6869 6e67 206d 6f72 6520 6578 6369 ething more exci\n+000038e0: 7469 6e67 2e20 20e2 8098 536b 6574 6368 ting. ...Sketch\n+000038f0: e280 9920 6861 7320 6e6f 206e 6f74 696f ... has no notio\n+00003900: 6e20 6f66 2061 2073 6f6c 6964 2c0a 6275 n of a solid,.bu\n+00003910: 7420 706f 6c79 676f 6e61 6c20 e280 9c66 t polygonal ...f\n+00003920: 6163 6573 e280 9d20 6361 6e20 6265 2075 aces... can be u\n+00003930: 7365 6420 746f 2072 6570 7265 7365 6e74 sed to represent\n+00003940: 2074 6865 2062 6f75 6e64 6172 7920 6f66 the boundary of\n+00003950: 2061 2073 6f6c 6964 2e0a 546f 2074 6865 a solid..To the\n+00003960: 2070 7265 7669 6f75 7320 6578 616d 706c previous exampl\n+00003970: 652c 206c 6574 2773 2061 6464 2074 6872 e, let's add thr\n+00003980: 6565 206d 6f72 6520 7472 6961 6e67 756c ee more triangul\n+00003990: 6172 2070 6f6c 7967 6f6e 7320 746f 0a6d ar polygons to.m\n+000039a0: 616b 6520 7468 6520 6661 6365 7320 6f66 ake the faces of\n+000039b0: 2061 6e20 6972 7265 6775 6c61 7220 7465 an irregular te\n+000039c0: 7472 6168 6564 726f 6e2e 0a20 2025 2076 trahedron.. % v\n+000039d0: 6572 7469 6365 7320 6f66 2074 6865 2074 ertices of the t\n+000039e0: 6574 7261 6865 6472 6f6e 0a20 2064 6566 etrahedron. def\n+000039f0: 2070 3120 2830 2c30 2c31 2920 6465 6620 p1 (0,0,1) def \n+00003a00: 7032 2028 312c 302c 3029 0a20 2064 6566 p2 (1,0,0). def\n+00003a10: 2070 3320 2830 2c31 2c30 2920 6465 6620 p3 (0,1,0) def \n+00003a20: 7034 2028 2d2e 332c 2d2e 352c 2d2e 3829 p4 (-.3,-.5,-.8)\n+00003a30: 0a0a 2020 2520 6661 6365 7320 6f66 2074 .. % faces of t\n+00003a40: 6865 2074 6574 7261 6865 6472 6f6e 2e0a he tetrahedron..\n+00003a50: 2020 706f 6c79 676f 6e28 7031 2928 7032 polygon(p1)(p2\n+00003a60: 2928 7033 2920 2520 6f72 6967 696e 616c )(p3) % original\n+00003a70: 2066 726f 6e74 2070 6f6c 7967 6f6e 0a20 front polygon. \n+00003a80: 2070 6f6c 7967 6f6e 2870 3129 2870 3429 polygon(p1)(p4)\n+00003a90: 2870 3229 2025 2062 6f74 746f 6d0a 2020 (p2) % bottom. \n+00003aa0: 706f 6c79 676f 6e28 7031 2928 7033 2928 polygon(p1)(p3)(\n+00003ab0: 7034 2920 2520 6c65 6674 0a20 2070 6f6c p4) % left. pol\n+00003ac0: 7967 6f6e 2870 3329 2870 3229 2870 3429 ygon(p3)(p2)(p4)\n+00003ad0: 2025 2072 6561 720a 0a20 2025 206c 696e % rear.. % lin\n+00003ae0: 6520 746f 2070 6965 7263 6520 7468 6520 e to pierce the \n+00003af0: 7465 7472 6168 6564 726f 6e0a 2020 6c69 tetrahedron. li\n+00003b00: 6e65 5b6c 696e 6563 6f6c 6f72 3d72 6564 ne[linecolor=red\n+00003b10: 5d28 2d31 2c2d 312c 2d31 2928 322c 322c ](-1,-1,-1)(2,2,\n+00003b20: 3229 0a54 6869 7320 6578 616d 706c 6520 2).This example \n+00003b30: 7573 6573 20e2 809c 6465 6669 6e69 7469 uses ...definiti\n+00003b40: 6f6e 73e2 809d 2c20 7768 6963 6820 6265 ons..., which be\n+00003b50: 6769 6e20 7769 7468 20e2 8098 6465 66e2 gin with ...def.\n+00003b60: 8099 2e20 2054 6865 7365 20e2 809c 6465 ... These ...de\n+00003b70: 6669 6e65 e280 9d0a 6f72 2067 6976 6520 fine....or give \n+00003b80: 6e61 6d65 7320 746f 2070 6f69 6e74 732c names to points,\n+00003b90: 2077 6869 6368 2061 7265 2074 6865 6e20 which are then \n+00003ba0: 6176 6169 6c61 626c 6520 6173 20e2 809c available as ...\n+00003bb0: 7265 6665 7265 6e63 6573 e280 9d20 6279 references... by\n+00003bc0: 0a65 6e63 6c6f 7369 6e67 2074 6865 206e .enclosing the n\n+00003bd0: 616d 6573 2069 6e20 7061 7265 6e74 6865 ames in parenthe\n+00003be0: 7365 732c 2065 2e67 2e20 2866 6f6f 292e ses, e.g. (foo).\n+00003bf0: 2020 5468 6520 7061 7265 6e74 6865 7365 The parenthese\n+00003c00: 7320 6465 6e6f 7465 0a74 6861 7420 7468 s denote.that th\n+00003c10: 6520 6e61 6d65 7320 7265 6665 7220 746f e names refer to\n+00003c20: 2070 6f69 6e74 733b 2074 6865 7920 6172 points; they ar\n+00003c30: 6520 7265 7175 6972 6564 2e20 2054 6865 e required. The\n+00003c40: 7265 2063 616e 2062 6520 6e6f 0a77 6869 re can be no.whi\n+00003c50: 7465 2073 7061 6365 2062 6574 7765 656e te space between\n+00003c60: 2074 6865 6d20 616e 6420 7468 6520 6e61 them and the na\n+00003c70: 6d65 2e0a 0a20 2020 4173 2079 6f75 2063 me... As you c\n+00003c80: 616e 2073 6565 2c20 636f 6d6d 656e 7473 an see, comments\n+00003c90: 2073 7461 7274 2077 6974 6820 2520 6173 start with % as\n+00003ca0: 2069 6e20 5465 5820 616e 6420 6578 7465 in TeX and exte\n+00003cb0: 6e64 2074 6f20 7468 6520 656e 640a 6f66 nd to the end.of\n+00003cc0: 2074 6865 206c 696e 6520 2874 686f 7567 the line (thoug\n+00003cd0: 6820 2320 7769 6c6c 2077 6f72 6b20 6173 h # will work as\n+00003ce0: 2077 656c 6c29 2e20 2057 6869 7465 2073 well). White s\n+00003cf0: 7061 6365 2c20 696e 636c 7564 696e 670a pace, including.\n+00003d00: 7370 6163 6573 2c20 7461 6273 2061 6e64 spaces, tabs and\n+00003d10: 2062 6c61 6e6b 206c 696e 6573 2c20 6861 blank lines, ha\n+00003d20: 7320 6e6f 2065 6666 6563 7420 696e 2074 s no effect in t\n+00003d30: 6865 20e2 8098 736b 6574 6368 e280 9920 he ...sketch... \n+00003d40: 6c61 6e67 7561 6765 2e0a 0a00 085b 696d language.....[im\n+00003d50: 6167 6520 7372 633d 2265 7830 3430 2e70 age src=\"ex040.p\n+00003d60: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n+00003d70: 6578 3034 3020 6f6d 6974 7465 6420 696e ex040 omitted in\n+00003d80: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n+00003d90: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n+00003da0: 0008 5d0a 0a49 6620 7765 206c 6f6f 6b20 ..]..If we look \n+00003db0: 696e 7369 6465 2074 6865 2054 6558 2066 inside the TeX f\n+00003dc0: 696c 6520 7072 6f64 7563 6564 2062 7920 ile produced by \n+00003dd0: e280 9873 6b65 7463 68e2 8099 2c20 7468 ...sketch..., th\n+00003de0: 6572 6520 7769 6c6c 2062 6520 6f6e 6c79 ere will be only\n+00003df0: 0a74 6872 6565 2070 6f6c 7967 6f6e 732e .three polygons.\n+00003e00: 2020 5468 6520 666f 7572 7468 2068 6173 The fourth has\n+00003e10: 2062 6565 6e20 6375 6c6c 6564 2062 6563 been culled bec\n+00003e20: 6175 7365 2069 7420 6973 2061 2022 6261 ause it is a \"ba\n+00003e30: 636b 2066 6163 6522 0a6f 6620 7468 6520 ck face\".of the \n+00003e40: 7465 7472 6168 6564 726f 6e2c 2069 6e76 tetrahedron, inv\n+00003e50: 6973 6962 6c65 2074 6f20 6f75 7220 7669 isible to our vi\n+00003e60: 6577 2e20 2049 7420 6973 2075 6e6e 6563 ew. It is unnec\n+00003e70: 6573 7361 7279 2c20 616e 6420 736f 2069 essary, and so i\n+00003e80: 740a 6973 2072 656d 6f76 6564 2e0a 0a20 t.is removed... \n+00003e90: 2020 496e 2073 6f6d 6520 6472 6177 696e In some drawin\n+00003ea0: 6773 2c20 706f 6c79 676f 6e73 2061 6374 gs, polygons act\n+00003eb0: 2061 7320 7a65 726f 2d74 6869 636b 6e65 as zero-thickne\n+00003ec0: 7373 2073 6f6c 6964 2073 7572 6661 6365 ss solid surface\n+00003ed0: 7320 7769 7468 0a62 6f74 6820 7369 6465 s with.both side\n+00003ee0: 7320 7669 7369 626c 6520 7261 7468 6572 s visible rather\n+00003ef0: 2074 6861 6e20 6173 2074 6865 2066 6163 than as the fac\n+00003f00: 6573 206f 6620 736f 6c69 6420 6f62 6a65 es of solid obje\n+00003f10: 6374 732c 2077 6865 7265 2062 6163 6b0a cts, where back.\n+00003f20: 6661 6365 7320 6361 6e20 6265 2063 756c faces can be cul\n+00003f30: 6c65 642e 2020 466f 7220 7a65 726f 2d74 led. For zero-t\n+00003f40: 6869 636b 6e65 7373 2073 6f6c 6964 732c hickness solids,\n+00003f50: 2063 756c 6c69 6e67 2069 7320 6120 7072 culling is a pr\n+00003f60: 6f62 6c65 6d2e 0a4f 6e65 2073 6f6c 7574 oblem..One solut\n+00003f70: 696f 6e20 6973 2074 6f20 7573 6520 6120 ion is to use a \n+00003f80: 7061 6972 206f 6620 e280 9873 6b65 7463 pair of ...sketc\n+00003f90: 68e2 8099 2070 6f6c 7967 6f6e 7320 666f h... polygons fo\n+00003fa0: 7220 6561 6368 0a7a 6572 6f2d 7468 6963 r each.zero-thic\n+00003fb0: 6b6e 6573 7320 6661 6365 2c20 6964 656e kness face, iden\n+00003fc0: 7469 6361 6c20 6578 6365 7074 2077 6974 tical except wit\n+00003fd0: 6820 6f70 706f 7369 7465 2076 6572 7465 h opposite verte\n+00003fe0: 7820 6f72 6465 7273 2e20 2054 6869 730a x orders. This.\n+00003ff0: 6973 2075 6e77 6965 6c64 7920 616e 6420 is unwieldy and \n+00004000: 6578 7065 6e73 6976 652e 2020 4120 6265 expensive. A be\n+00004010: 7474 6572 2077 6179 2069 7320 746f 2073 tter way is to s\n+00004020: 6574 2074 6865 20e2 8098 736b 6574 6368 et the ...sketch\n+00004030: e280 9920 696e 7465 726e 616c 0a6f 7074 ... internal.opt\n+00004040: 696f 6e20 e280 9863 756c 6ce2 8099 2074 ion ...cull... t\n+00004050: 6f20 e280 9866 616c 7365 e280 9920 696e o ...false... in\n+00004060: 2074 6865 2075 7375 616c 20e2 8098 5053 the usual ...PS\n+00004070: 5472 6963 6b73 e280 9920 6d61 6e6e 6572 Tricks... manner\n+00004080: 2e0a 2020 706f 6c79 676f 6e5b 6375 6c6c .. polygon[cull\n+00004090: 3d66 616c 7365 5d28 7031 2928 7032 2928 =false](p1)(p2)(\n+000040a0: 7033 290a 5468 6520 666f 6c6c 6f77 696e p3).The followin\n+000040b0: 6720 7368 6f77 7320 7468 6520 7361 6d65 g shows the same\n+000040c0: 2068 656c 6978 2073 6861 7065 2064 7261 helix shape dra\n+000040d0: 776e 2066 6972 7374 2077 6974 6820 6375 wn first with cu\n+000040e0: 6c6c 3d74 7275 6520 2874 6865 0a64 6566 ll=true (the.def\n+000040f0: 6175 6c74 2920 616e 6420 7468 656e 2063 ault) and then c\n+00004100: 756c 6c3d 6661 6c73 652e 0a0a 0008 5b69 ull=false.....[i\n+00004110: 6d61 6765 2073 7263 3d22 6578 3034 352e mage src=\"ex045.\n+00004120: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n+00004130: 2065 7830 3435 206f 6d69 7474 6564 2069 ex045 omitted i\n+00004140: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n+00004150: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n+00004160: 2200 085d 0a0a 5765 276c 6c20 736f 6f6e \"..]..We'll soon\n+00004170: 2073 6565 2068 6f77 2074 6f20 7072 6f64 see how to prod\n+00004180: 7563 6520 7468 6573 6520 6865 6c69 7865 uce these helixe\n+00004190: 7320 7769 7468 2061 2066 6577 206c 696e s with a few lin\n+000041a0: 6573 206f 6620 e280 9873 6b65 7463 68e2 es of ...sketch.\n+000041b0: 8099 0a6c 616e 6775 6167 6520 636f 6465 ...language code\n+000041c0: 2e0a 0a20 2020 4974 206d 6179 2062 6520 ... It may be \n+000041d0: 7465 6d70 7469 6e67 2074 6f20 7475 726e tempting to turn\n+000041e0: 2063 756c 6c69 6e67 206f 6666 2067 7261 culling off gra\n+000041f0: 7475 6974 6f75 736c 7920 736f 2074 6861 tuitously so tha\n+00004200: 7420 7665 7274 6578 0a6f 7264 6572 2063 t vertex.order c\n+00004210: 616e 2062 6520 6967 6e6f 7265 642e 2020 an be ignored. \n+00004220: 5468 6973 2069 7320 6e6f 7420 6120 676f This is not a go\n+00004230: 6f64 2069 6465 6120 6265 6361 7573 6520 od idea because \n+00004240: 6f75 7470 7574 2066 696c 6520 7369 7a65 output file size\n+00004250: 0a61 6e64 2054 6558 2061 6e64 2050 6f73 .and TeX and Pos\n+00004260: 7473 6372 6970 7420 7072 6f63 6573 7369 tscript processi\n+00004270: 6e67 2074 696d 6520 626f 7468 2064 6570 ng time both dep\n+00004280: 656e 6420 6f6e 2074 6865 206e 756d 6265 end on the numbe\n+00004290: 7220 6f66 0a6f 7574 7075 7420 706f 6c79 r of.output poly\n+000042a0: 676f 6e73 2e20 2043 756c 6c69 6e67 2075 gons. Culling u\n+000042b0: 7375 616c 6c79 2069 6d70 726f 7665 7320 sually improves \n+000042c0: 7065 7266 6f72 6d61 6e63 6520 6279 2061 performance by a\n+000042d0: 2066 6163 746f 7220 6f66 0a74 776f 2e20 factor of.two. \n+000042e0: 204f 6e20 7468 6520 6f74 6865 7220 6861 On the other ha\n+000042f0: 6e64 2c20 676c 6f62 616c 6c79 2073 6574 nd, globally set\n+00004300: 7469 6e67 20e2 8098 6375 6c6c 3d66 616c ting ...cull=fal\n+00004310: 7365 e280 9920 6973 2072 6561 736f 6e61 se... is reasona\n+00004320: 626c 650a 7768 696c 6520 6465 6275 6767 ble.while debugg\n+00004330: 696e 672e 2020 5365 6520 2a6e 6f74 6520 ing. See *note \n+00004340: 476c 6f62 616c 206f 7074 696f 6e73 3a3a Global options::\n+00004350: 2061 6e64 202a 6e6f 7465 204c 696d 6974 and *note Limit\n+00004360: 7320 6f6e 2065 7272 6f72 0a64 6574 6563 s on error.detec\n+00004370: 7469 6f6e 3a3a 2e0a 0a1f 0a46 696c 653a tion::.....File:\n+00004380: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+00004390: 6f64 653a 2053 7065 6369 616c 206f 626a ode: Special obj\n+000043a0: 6563 7473 2c20 204e 6578 743a 204f 626a ects, Next: Obj\n+000043b0: 6563 7420 7472 616e 7366 6f72 6d73 2c20 ect transforms, \n+000043c0: 2050 7265 763a 2044 7261 7769 6e67 2061 Prev: Drawing a\n+000043d0: 2073 6f6c 6964 2c20 2055 703a 2049 6e74 solid, Up: Int\n+000043e0: 726f 6475 6374 696f 6e20 6279 2065 7861 roduction by exa\n+000043f0: 6d70 6c65 0a0a 322e 3420 5370 6563 6961 mple..2.4 Specia\n+00004400: 6c20 6f62 6a65 6374 730a 3d3d 3d3d 3d3d l objects.======\n+00004410: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0a57 =============..W\n+00004420: 6520 6361 6e20 6164 6420 6c61 6265 6c73 e can add labels\n+00004430: 2074 6f20 6120 6472 6177 696e 6720 6279 to a drawing by\n+00004440: 2075 7369 6e67 2073 7065 6369 616c 206f using special o\n+00004450: 626a 6563 7473 2c20 7768 6963 6820 7072 bjects, which pr\n+00004460: 6f76 6964 6520 610a 7761 7920 746f 2065 ovide a.way to e\n+00004470: 6d62 6564 2072 6177 204c 6154 6558 2061 mbed raw LaTeX a\n+00004480: 6e64 20e2 8098 5053 5472 6963 6b73 e280 nd ...PSTricks..\n+00004490: 9920 636f 6465 2e20 2041 6464 696e 6720 . code. Adding \n+000044a0: 7468 6973 2074 6f20 7468 650a 7465 7472 this to the.tetr\n+000044b0: 6168 6564 726f 6e20 646f 6573 2074 6865 ahedron does the\n+000044c0: 2074 7269 636b 2e0a 2020 7370 6563 6961 trick.. specia\n+000044d0: 6c20 7c5c 666f 6f74 6e6f 7465 7369 7a65 l |\\footnotesize\n+000044e0: 0a20 2020 2020 2020 2020 2020 5c75 7075 . \\upu\n+000044f0: 747b 3270 747d 5b75 725d 2331 7b24 5031 t{2pt}[ur]#1{$P1\n+00004500: 247d 0a20 2020 2020 2020 2020 2020 5c75 $}. \\u\n+00004510: 7075 745b 725d 2332 7b24 5032 247d 0a20 put[r]#2{$P2$}. \n+00004520: 2020 2020 2020 2020 2020 5c75 7075 745b \\uput[\n+00004530: 755d 2333 7b24 5033 247d 0a20 2020 2020 u]#3{$P3$}. \n+00004540: 2020 2020 2020 5c75 7075 745b 645d 2334 \\uput[d]#4\n+00004550: 7b24 5034 247d 7c0a 2020 2020 2870 3129 {$P4$}|. (p1)\n+00004560: 2870 3229 2870 3329 2870 3429 0a48 6572 (p2)(p3)(p4).Her\n+00004570: 6520 6973 2074 6865 2072 6573 756c 742e e is the result.\n+00004580: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22 ....[image src=\"\n+00004590: 6578 3034 322e 706e 6722 2074 6578 743d ex042.png\" text=\n+000045a0: 2249 6d61 6765 2065 7830 3432 206f 6d69 \"Image ex042 omi\n+000045b0: 7474 6564 2069 6e20 7465 7874 2076 6572 tted in text ver\n+000045c0: 7369 6f6e 206f 6620 7468 6973 2064 6f63 sion of this doc\n+000045d0: 756d 656e 742e 2200 085d 0a0a 2020 2054 ument.\"..].. T\n+000045e0: 6865 7265 2061 7265 2073 6576 6572 616c here are several\n+000045f0: 2064 6574 6169 6c73 2074 6f20 6e6f 7465 details to note\n+00004600: 2068 6572 652e 2020 4669 7273 742c 2074 here. First, t\n+00004610: 6865 2071 756f 7469 6e67 0a63 6f6e 7665 he quoting.conve\n+00004620: 6e74 696f 6e20 666f 7220 7468 6520 7261 ntion for the ra\n+00004630: 7720 636f 6465 2069 7320 7369 6d69 6c61 w code is simila\n+00004640: 7220 746f 2074 6865 204c 6154 6558 205c r to the LaTeX \\\n+00004650: 7665 7262 2063 6f6d 6d61 6e64 2e20 2054 verb command. T\n+00004660: 6865 0a66 6972 7374 206e 6f6e 2d77 6869 he.first non-whi\n+00004670: 7465 2073 7061 6365 2063 6861 7261 6374 te space charact\n+00004680: 6572 2066 6f6c 6c6f 7769 6e67 2073 7065 er following spe\n+00004690: 6369 616c 2069 7320 756e 6465 7273 746f cial is understo\n+000046a0: 6f64 2074 6f20 6265 0a74 6865 2071 756f od to be.the quo\n+000046b0: 7465 2063 6861 7261 6374 6572 2c20 696e te character, in\n+000046c0: 2074 6869 7320 6361 7365 20e2 8098 7ce2 this case ...|.\n+000046d0: 8099 2e20 2054 6865 2072 6177 2074 6578 ... The raw tex\n+000046e0: 7420 636f 6e74 696e 7565 7320 756e 7469 t continues unti\n+000046f0: 6c0a 7468 6973 2063 6861 7261 6374 6572 l.this character\n+00004700: 2072 6563 7572 732e 0a0a 2020 2053 6563 recurs... Sec\n+00004710: 6f6e 642c 2074 6865 2061 7267 756d 656e ond, the argumen\n+00004720: 7420 7265 6665 7265 6e63 6573 2023 312c t references #1,\n+00004730: 2023 322c 2023 332c 2061 6e64 2023 3420 #2, #3, and #4 \n+00004740: 7265 6665 7220 746f 2070 6f69 6e74 2c0a refer to point,.\n+00004750: 7665 6374 6f72 2c20 6f72 2073 6361 6c61 vector, or scala\n+00004760: 7220 7661 6c75 6573 2069 6e20 7468 6520 r values in the \n+00004770: 6c69 7374 2074 6861 7420 666f 6c6c 6f77 list that follow\n+00004780: 2e20 2054 6869 7320 6973 2073 696d 696c . This is simil\n+00004790: 6172 2074 6f0a 5465 5820 6d61 6372 6f20 ar to.TeX macro \n+000047a0: 7379 6e74 6178 2e20 2054 6865 2074 7261 syntax. The tra\n+000047b0: 6e73 666f 726d 6564 2061 6e64 2074 776f nsformed and two\n+000047c0: 2d64 696d 656e 7369 6f6e 616c 2070 726f -dimensional pro\n+000047d0: 6a65 6374 696f 6e73 206f 660a 7468 6573 jections of.thes\n+000047e0: 6520 7468 7265 652d 6469 6d65 6e73 696f e three-dimensio\n+000047f0: 6e61 6c20 706f 696e 7473 2061 7265 2073 nal points are s\n+00004800: 7562 7374 6974 7574 6564 2069 6e20 7468 ubstituted in th\n+00004810: 6520 6669 6e61 6c20 6f75 7470 7574 2e20 e final output. \n+00004820: 2041 6e0a 6172 6775 6d65 6e74 2072 6566 An.argument ref\n+00004830: 6572 656e 6365 206f 6620 7468 6520 666f erence of the fo\n+00004840: 726d 2023 312d 3220 6973 2072 6570 6c61 rm #1-2 is repla\n+00004850: 6365 6420 7769 7468 2074 6865 2061 6e67 ced with the ang\n+00004860: 6c65 2069 6e0a 6465 6772 6565 7320 6f66 le in.degrees of\n+00004870: 2074 6865 2074 776f 2d64 696d 656e 7369 the two-dimensi\n+00004880: 6f6e 616c 2076 6563 746f 7220 7468 6174 onal vector that\n+00004890: 2063 6f6e 6e65 6374 7320 7468 6520 7072 connects the pr\n+000048a0: 6f6a 6563 7469 6f6e 7320 6f66 0a74 6865 ojections of.the\n+000048b0: 2074 776f 2072 6573 7065 6374 6976 6520 two respective \n+000048c0: 6172 6775 6d65 6e74 2070 6f69 6e74 732c argument points,\n+000048d0: 2068 6572 6520 2331 2061 6e64 2023 322e here #1 and #2.\n+000048e0: 2020 5468 6520 7375 6273 7469 7475 7465 The substitute\n+000048f0: 640a 616e 676c 6520 6973 2065 6e63 6c6f d.angle is enclo\n+00004900: 7365 6420 696e 2063 7572 6c79 2062 7261 sed in curly bra\n+00004910: 6365 7320 e280 987b 207d e280 992e 2020 ces ...{ }.... \n+00004920: 5768 656e 20e2 8098 5469 6b5a 2f50 4746 When ...TikZ/PGF\n+00004930: e280 9920 6f75 7470 7574 2069 730a 6265 ... output is.be\n+00004940: 696e 6720 6765 6e65 7261 7465 642c 2074 ing generated, t\n+00004950: 6865 2061 6e67 6c65 2069 7320 726f 756e he angle is roun\n+00004960: 6465 6420 746f 2074 6865 206e 6561 7265 ded to the neare\n+00004970: 7374 2064 6567 7265 6520 6265 6361 7573 st degree becaus\n+00004980: 650a 6e6f 6e2d 696e 7465 6765 7220 616e e.non-integer an\n+00004990: 676c 6573 2061 7265 206e 6f74 2061 6c6c gles are not all\n+000049a0: 6f77 6564 2062 7920 e280 9854 696b 5a2f owed by ...TikZ/\n+000049b0: 5047 46e2 8099 2070 7269 6d69 7469 7665 PGF... primitive\n+000049c0: 732e 0a0a 2020 2041 7320 6f66 2056 6572 s... As of Ver\n+000049d0: 7369 6f6e 2030 2e33 206f 6620 e280 9873 sion 0.3 of ...s\n+000049e0: 6b65 7463 68e2 8099 2c20 7370 6563 6961 ketch..., specia\n+000049f0: 6c20 6172 6775 6d65 6e74 7320 6d61 7920 l arguments may \n+00004a00: 6265 2073 6361 6c61 7273 206f 720a 7665 be scalars or.ve\n+00004a10: 6374 6f72 7320 696e 2061 6464 6974 696f ctors in additio\n+00004a20: 6e20 746f 2070 6f69 6e74 732e 2020 5265 n to points. Re\n+00004a30: 6665 7265 6e63 6573 2074 6f20 7363 616c ferences to scal\n+00004a40: 6172 2061 7267 756d 656e 7473 2061 7265 ar arguments are\n+00004a50: 0a6d 6572 656c 7920 7265 706c 6163 6564 .merely replaced\n+00004a60: 2077 6974 6820 6120 6e75 6d62 6572 2066 with a number f\n+00004a70: 6f72 6d61 7474 6564 206a 7573 7420 6173 ormatted just as\n+00004a80: 2061 6e79 2070 6f69 6e74 2063 6f6f 7264 any point coord\n+00004a90: 696e 6174 652e 0a52 6566 6572 656e 6365 inate..Reference\n+00004aa0: 7320 746f 2076 6563 746f 7273 2062 6563 s to vectors bec\n+00004ab0: 6f6d 6520 7477 6f2d 6469 6d65 6e73 696f ome two-dimensio\n+00004ac0: 6e61 6c20 706f 696e 7473 2e20 2054 6865 nal points. The\n+00004ad0: 2074 6963 6b20 6f70 6572 6174 6f72 0a74 tick operator.t\n+00004ae0: 6861 7420 7365 6c65 6374 7320 696e 6469 hat selects indi\n+00004af0: 7669 6475 616c 2063 6f6d 706f 6e65 6e74 vidual component\n+00004b00: 7320 6f66 2070 6f69 6e74 7320 616e 6420 s of points and \n+00004b10: 7665 6374 6f72 7320 656c 7365 7768 6572 vectors elsewher\n+00004b20: 6520 696e 0ae2 8098 736b 6574 6368 e280 e in....sketch..\n+00004b30: 9920 2873 6565 2066 6f72 2065 7861 6d70 . (see for examp\n+00004b40: 6c65 202a 6e6f 7465 2041 6666 696e 6520 le *note Affine \n+00004b50: 6172 6974 686d 6574 6963 3a3a 2920 6361 arithmetic::) ca\n+00004b60: 6e20 616c 736f 2062 6520 6170 706c 6965 n also be applie\n+00004b70: 640a 746f 2070 6f69 6e74 2061 6e64 2076 d.to point and v\n+00004b80: 6563 746f 7220 6172 6775 6d65 6e74 2072 ector argument r\n+00004b90: 6566 6572 656e 6365 732e 2020 416c 6c20 eferences. All \n+00004ba0: 7468 7265 6520 6469 6d65 6e73 696f 6e73 three dimensions\n+00004bb0: 206f 6620 610a 7472 616e 7366 6f72 6d65 of a.transforme\n+00004bc0: 6420 706f 696e 7420 6f72 2076 6563 746f d point or vecto\n+00004bd0: 7220 6361 6e20 616c 736f 2062 6520 7375 r can also be su\n+00004be0: 6273 7469 7475 6564 2077 6974 6820 e280 bstitued with ..\n+00004bf0: 9827 33e2 8099 2e20 2053 6565 202a 6e6f .'3.... See *no\n+00004c00: 7465 0a53 7065 6369 616c 733a 3a20 666f te.Specials:: fo\n+00004c10: 7220 6465 7461 696c 732e 0a0a 2020 2042 r details... B\n+00004c20: 7920 6465 6661 756c 742c 20e2 8098 7370 y default, ...sp\n+00004c30: 6563 6961 6ce2 8099 206f 626a 6563 7473 ecial... objects\n+00004c40: 2061 7265 2070 7269 6e74 6564 206c 6173 are printed las\n+00004c50: 742c 206f 7665 726c 6179 696e 6720 616c t, overlaying al\n+00004c60: 6c20 6f74 6865 720a 6f62 6a65 6374 7320 l other.objects \n+00004c70: 696e 2074 6865 2073 6365 6e65 2e20 2049 in the scene. I\n+00004c80: 6620 796f 7520 7370 6563 6966 7920 7468 f you specify th\n+00004c90: 6520 696e 7465 726e 616c 206f 7074 696f e internal optio\n+00004ca0: 6e20 e280 986c 6179 3d69 6ee2 8099 2c20 n ...lay=in..., \n+00004cb0: 7468 650a 6869 6464 656e 2073 7572 6661 the.hidden surfa\n+00004cc0: 6365 2061 6c67 6f72 6974 686d 2063 6f6e ce algorithm con\n+00004cd0: 7369 6465 7273 2074 6865 2065 6e74 6972 siders the entir\n+00004ce0: 6520 7370 6563 6961 6c20 6f62 6a65 6374 e special object\n+00004cf0: 2074 6f20 6265 2074 6865 0a66 6972 7374 to be the.first\n+00004d00: 2070 6f69 6e74 2028 2331 2920 696e 2074 point (#1) in t\n+00004d10: 6865 2061 7267 756d 656e 7420 6c69 7374 he argument list\n+00004d20: 2e20 2049 6620 7468 6174 2070 6f69 6e74 . If that point\n+00004d30: 2069 7320 6265 6869 6e64 2028 6f66 0a73 is behind (of.s\n+00004d40: 6d61 6c6c 6572 207a 2d63 6f6d 706f 6e65 maller z-compone\n+00004d50: 6e74 2074 6861 6e29 2061 6e79 2064 7261 nt than) any dra\n+00004d60: 7761 626c 652c 2074 6865 6e20 7468 6520 wable, then the \n+00004d70: 656e 7469 7265 2073 7065 6369 616c 206f entire special o\n+00004d80: 626a 6563 740a 6973 2064 7261 776e 2062 bject.is drawn b\n+00004d90: 6566 6f72 6520 7468 6174 2064 7261 7761 efore that drawa\n+00004da0: 626c 652c 2073 6f20 7468 6520 6472 6177 ble, so the draw\n+00004db0: 6162 6c65 206f 6273 6375 7265 7320 7061 able obscures pa\n+00004dc0: 7274 7320 6f66 2074 6865 0a73 7065 6369 rts of the.speci\n+00004dd0: 616c 206f 626a 6563 7420 7468 6174 206f al object that o\n+00004de0: 7665 726c 6170 7320 6974 2e20 2049 6e20 verlaps it. In \n+00004df0: 6f75 7220 6578 616d 706c 652c 2070 3120 our example, p1 \n+00004e00: 6973 2074 6865 2066 726f 6e74 2d6d 6f73 is the front-mos\n+00004e10: 740a 706f 696e 7420 696e 2074 6865 2073 t.point in the s\n+00004e20: 6365 6e65 2028 6861 7320 7468 6520 6c61 cene (has the la\n+00004e30: 7267 6573 7420 7a2d 636f 6d70 6f6e 656e rgest z-componen\n+00004e40: 7429 2c20 736f 2061 6464 696e 6720 e280 t), so adding ..\n+00004e50: 986c 6179 3d69 6ee2 8099 2068 6173 0a6e .lay=in... has.n\n+00004e60: 6f20 6566 6665 6374 2e0a 0a20 2020 5769 o effect... Wi\n+00004e70: 7468 206f 7074 696f 6e20 e280 986c 6179 th option ...lay\n+00004e80: 3d75 6e64 6572 e280 992c 2061 2073 7065 =under..., a spe\n+00004e90: 6369 616c 2069 7320 6472 6177 6e20 5f62 cial is drawn _b\n+00004ea0: 6566 6f72 655f 2c20 6865 6e63 6520 6170 efore_, hence ap\n+00004eb0: 7065 6172 730a 5f75 6e64 6572 5f20 616e pears._under_ an\n+00004ec0: 7920 6f66 2074 6865 206f 626a 6563 7473 y of the objects\n+00004ed0: 2068 616e 646c 6564 2062 7920 7468 6520 handled by the \n+00004ee0: 6869 6464 656e 2073 7572 6661 6365 2061 hidden surface a\n+00004ef0: 6c67 6f72 6974 686d 2e0a 5468 6973 2069 lgorithm..This i\n+00004f00: 7320 686f 7720 7468 6520 6c69 6768 7420 s how the light \n+00004f10: 6772 6179 2061 7865 7320 7765 7265 2061 gray axes were a\n+00004f20: 6464 6564 2074 6f20 7468 6520 2268 656c dded to the \"hel\n+00004f30: 6c6f 2077 6f72 6c64 2220 6578 616d 706c lo world\" exampl\n+00004f40: 650a 2a6e 6f74 6520 4865 6c6c 6f20 776f e.*note Hello wo\n+00004f50: 726c 643a 3a2e 0a0a 2020 2053 7065 6369 rld::... Speci\n+00004f60: 616c 206f 626a 6563 7473 2061 7265 2070 al objects are p\n+00004f70: 6f77 6572 6675 6c2c 2077 6974 6820 6d61 owerful, with ma\n+00004f80: 6e79 2070 6f73 7369 626c 6520 7573 6573 ny possible uses\n+00004f90: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n+00004fa0: 682e 696e 666f 2c20 204e 6f64 653a 204f h.info, Node: O\n+00004fb0: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n+00004fc0: 2c20 204e 6578 743a 2052 6570 6561 7465 , Next: Repeate\n+00004fd0: 6420 6f62 6a65 6374 732c 2020 5072 6576 d objects, Prev\n+00004fe0: 3a20 5370 6563 6961 6c20 6f62 6a65 6374 : Special object\n+00004ff0: 732c 2020 5570 3a20 496e 7472 6f64 7563 s, Up: Introduc\n+00005000: 7469 6f6e 2062 7920 6578 616d 706c 650a tion by example.\n+00005010: 0a32 2e35 2054 7261 6e73 666f 726d 730a .2.5 Transforms.\n+00005020: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a ==============..\n+00005030: 4e6f 7720 6c65 7427 7320 6164 6420 6120 Now let's add a \n+00005040: 7365 636f 6e64 2063 6f70 7920 6f66 2074 second copy of t\n+00005050: 6865 2070 6965 7263 6564 2074 6574 7261 he pierced tetra\n+00005060: 6865 6472 6f6e 2e20 2057 6527 6c6c 2072 hedron. We'll r\n+00005070: 6f74 6174 650a 7468 6520 636f 7079 2039 otate.the copy 9\n+00005080: 3020 6465 6772 6565 7320 6162 6f75 7420 0 degrees about \n+00005090: 7468 6520 782d 6178 6973 2077 6974 6820 the x-axis with \n+000050a0: 7468 6520 6f72 6967 696e 2061 7320 e280 the origin as ..\n+000050b0: 9c63 656e 7465 7220 6f66 0a72 6f74 6174 .center of.rotat\n+000050c0: 696f 6ee2 809d 2073 6f20 7765 2063 616e ion... so we can\n+000050d0: 2073 6565 2074 6865 2062 6163 6b2c 2074 see the back, t\n+000050e0: 6865 6e20 7472 616e 736c 6174 6520 6974 hen translate it\n+000050f0: 2074 6f20 7468 6520 7269 6768 742d 2d69 to the right--i\n+00005100: 6e20 7468 650a 706f 7369 7469 7665 2078 n the.positive x\n+00005110: 2d64 6972 6563 7469 6f6e 2d2d 736f 2069 -direction--so i\n+00005120: 7420 646f 6573 6e27 7420 636f 6c6c 6964 t doesn't collid\n+00005130: 6520 7769 7468 2074 6865 206f 7269 6769 e with the origi\n+00005140: 6e61 6c2e 2020 546f 2068 656c 700a 7573 nal. To help.us\n+00005150: 2073 6565 2077 6861 7427 7320 676f 696e see what's goin\n+00005160: 6720 6f6e 2c20 6d61 6b65 2074 6865 2062 g on, make the b\n+00005170: 6163 6b20 7369 6465 2067 7261 792e 0a20 ack side gray.. \n+00005180: 2064 6566 2070 6965 7263 6564 5f74 6574 def pierced_tet\n+00005190: 7261 6865 6472 6f6e 207b 0a20 2020 2064 rahedron {. d\n+000051a0: 6566 2070 3120 2830 2c30 2c31 2920 6465 ef p1 (0,0,1) de\n+000051b0: 6620 7032 2028 312c 302c 3029 0a20 2020 f p2 (1,0,0). \n+000051c0: 2064 6566 2070 3320 2830 2c31 2c30 2920 def p3 (0,1,0) \n+000051d0: 6465 6620 7034 2028 2d2e 332c 2d2e 352c def p4 (-.3,-.5,\n+000051e0: 2d2e 3829 0a20 2020 2070 6f6c 7967 6f6e -.8). polygon\n+000051f0: 2870 3129 2870 3229 2870 3329 2020 2020 (p1)(p2)(p3) \n 00005200: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00005210: 2020 2020 2520 6f72 6967 696e 616c 0a20 % original. \n-00005220: 2020 2070 6f6c 7967 6f6e 2870 3129 2870 polygon(p1)(p\n-00005230: 3429 2870 3229 2020 2020 2020 2020 2020 4)(p2) \n-00005240: 2020 2020 2020 2020 2020 2020 2520 626f % bo\n-00005250: 7474 6f6d 0a20 2020 2070 6f6c 7967 6f6e ttom. polygon\n-00005260: 2870 3129 2870 3329 2870 3429 2020 2020 (p1)(p3)(p4) \n+00005210: 2020 2520 6f72 6967 696e 616c 0a20 2020 % original. \n+00005220: 2070 6f6c 7967 6f6e 2870 3129 2870 3429 polygon(p1)(p4)\n+00005230: 2870 3229 2020 2020 2020 2020 2020 2020 (p2) \n+00005240: 2020 2020 2020 2020 2020 2520 626f 7474 % bott\n+00005250: 6f6d 0a20 2020 2070 6f6c 7967 6f6e 2870 om. polygon(p\n+00005260: 3129 2870 3329 2870 3429 2020 2020 2020 1)(p3)(p4) \n 00005270: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00005280: 2020 2520 6c65 6674 0a20 2020 2070 6f6c % left. pol\n-00005290: 7967 6f6e 5b66 696c 6c63 6f6c 6f72 3d6c ygon[fillcolor=l\n-000052a0: 6967 6874 6772 6179 5d28 7033 2928 7032 ightgray](p3)(p2\n-000052b0: 2928 7034 2920 2520 7265 6172 0a20 2020 )(p4) % rear. \n-000052c0: 206c 696e 655b 6c69 6e65 636f 6c6f 723d line[linecolor=\n-000052d0: 7265 645d 282d 312c 2d31 2c2d 3129 2832 red](-1,-1,-1)(2\n-000052e0: 2c32 2c32 290a 2020 7d0a 2020 7b70 6965 ,2,2). }. {pie\n-000052f0: 7263 6564 5f74 6574 7261 6865 6472 6f6e rced_tetrahedron\n-00005300: 7d20 2025 2074 6574 7261 6865 6472 6f6e } % tetrahedron\n-00005310: 2069 6e20 6f72 6967 696e 616c 2070 6f73 in original pos\n-00005320: 6974 696f 6e0a 2020 7075 7420 7b20 726f ition. put { ro\n-00005330: 7461 7465 2839 302c 2028 302c 302c 3029 tate(90, (0,0,0)\n-00005340: 2c20 5b31 2c30 2c30 5d29 2025 2063 6f70 , [1,0,0]) % cop\n-00005350: 7920 696e 206e 6577 2070 6f73 6974 696f y in new positio\n-00005360: 6e0a 2020 2020 2020 2020 7468 656e 2074 n. then t\n-00005370: 7261 6e73 6c61 7465 285b 322e 352c 302c ranslate([2.5,0,\n-00005380: 305d 2920 7d20 7b70 6965 7263 6564 5f74 0]) } {pierced_t\n-00005390: 6574 7261 6865 6472 6f6e 7d0a 4865 7265 etrahedron}.Here\n-000053a0: 2074 6865 2065 6e74 6972 6520 636f 6465 the entire code\n-000053b0: 206f 6620 7468 6520 7072 6576 696f 7573 of the previous\n-000053c0: 2065 7861 6d70 6c65 2068 6173 2062 6565 example has bee\n-000053d0: 6e20 7772 6170 7065 6420 696e 2061 0a64 n wrapped in a.d\n-000053e0: 6566 696e 6974 696f 6e20 6279 2066 6f72 efinition by for\n-000053f0: 6d69 6e67 2061 20e2 809c 626c 6f63 6be2 ming a ...block.\n-00005400: 809d 2077 6974 6820 6272 6163 6573 2028 .. with braces (\n-00005410: 6120 7369 6e67 6c65 2069 7465 6d20 776f a single item wo\n-00005420: 756c 6420 6e6f 740a 6e65 6564 2074 6865 uld not.need the\n-00005430: 6d29 2e20 2054 6865 2070 6f69 6e74 2064 m). The point d\n-00005440: 6566 696e 6974 696f 6e73 206e 6573 7465 efinitions neste\n-00005450: 6420 696e 7369 6465 2074 6865 2062 7261 d inside the bra\n-00005460: 6365 7320 6172 650a e280 9c6c 6578 6963 ces are....lexic\n-00005470: 616c 6c79 2073 636f 7065 64e2 809d 2e20 ally scoped.... \n-00005480: 2054 6865 6972 206d 6561 6e69 6e67 2065 Their meaning e\n-00005490: 7874 656e 6473 206f 6e6c 7920 746f 2074 xtends only to t\n-000054a0: 6865 2065 6e64 206f 6620 7468 6520 626c he end of the bl\n-000054b0: 6f63 6b2e 0a54 6865 206f 7574 6572 2064 ock..The outer d\n-000054c0: 6566 2069 7320 6361 6c6c 6564 2061 20e2 ef is called a .\n-000054d0: 809c 6472 6177 6162 6c65 e280 9d20 6465 ..drawable... de\n-000054e0: 6669 6e69 7469 6f6e 2062 6563 6175 7365 finition because\n-000054f0: 2069 7420 6465 7363 7269 6265 730a 736f it describes.so\n-00005500: 6d65 7468 696e 6720 7468 6174 2063 616e mething that can\n-00005510: 2062 6520 6472 6177 6e2e 0a0a 2020 2041 be drawn... A\n-00005520: 2064 7261 7761 626c 6520 6465 6669 6e69 drawable defini\n-00005530: 7469 6f6e 2062 7920 6974 7365 6c66 2063 tion by itself c\n-00005540: 6175 7365 7320 6e6f 7468 696e 6720 746f auses nothing to\n-00005550: 2068 6170 7065 6e20 756e 7469 6c20 6974 happen until it\n-00005560: 730a 6e61 6d65 2069 7320 7265 6665 7265 s.name is refere\n-00005570: 6e63 6564 2e20 2044 7261 7761 626c 6520 nced. Drawable \n-00005580: 7265 6665 7265 6e63 6573 206d 7573 7420 references must \n-00005590: 6265 2065 6e63 6c6f 7365 6420 696e 2063 be enclosed in c\n-000055a0: 7572 6c79 0a62 7261 6365 732c 2065 2e67 urly.braces, e.g\n-000055b0: 2e20 7b66 6f6f 7d2c 2077 6974 6820 6e6f . {foo}, with no\n-000055c0: 2069 6e74 6572 7665 6e69 6e67 2077 6869 intervening whi\n-000055d0: 7465 2073 7061 6365 2e20 2049 6e20 7468 te space. In th\n-000055e0: 6520 636f 6465 2061 626f 7665 2c0a 7468 e code above,.th\n-000055f0: 6520 6669 7273 7420 7265 6665 7265 6e63 e first referenc\n-00005600: 6520 7b70 6965 7263 6564 5f74 6574 7261 e {pierced_tetra\n-00005610: 6865 6472 6f6e 7d20 6973 2061 2070 6c61 hedron} is a pla\n-00005620: 696e 206f 6e65 2e20 2049 7473 2065 6666 in one. Its eff\n-00005630: 6563 7420 6973 0a6d 6572 656c 7920 746f ect is.merely to\n-00005640: 2064 7570 6c69 6361 7465 2074 6865 2065 duplicate the e\n-00005650: 6172 6c69 6572 2064 7261 7769 6e67 2e20 arlier drawing. \n-00005660: 2041 6c6d 6f73 7420 616e 7920 7365 7269 Almost any seri\n-00005670: 6573 206f 6620 e280 9873 6b65 7463 68e2 es of ...sketch.\n-00005680: 8099 0a63 6f6d 6d61 6e64 7320 7374 7566 ...commands stuf\n-00005690: 6620 6d61 7920 6265 2072 6570 6c61 6365 f may be replace\n-000056a0: 6420 7769 7468 2064 6566 2066 6f6f 207b d with def foo {\n-000056b0: 2073 7475 6666 207d 207b 666f 6f7d 2077 stuff } {foo} w\n-000056c0: 6974 686f 7574 0a63 6861 6e67 696e 6720 ithout.changing \n-000056d0: 6974 7320 6d65 616e 696e 672e 0a0a 2020 its meaning... \n-000056e0: 2054 6865 2070 7574 2063 6f6d 6d61 6e64 The put command\n-000056f0: 2073 7570 706c 6965 7320 6120 7365 636f supplies a seco\n-00005700: 6e64 2072 6566 6572 656e 6365 2c20 7468 nd reference, th\n-00005710: 6973 2074 696d 6520 7769 7468 2061 0ae2 is time with a..\n-00005720: 809c 7472 616e 7366 6f72 6de2 809d 2061 ..transform... a\n-00005730: 7070 6c69 6564 2066 6972 7374 2e20 2054 pplied first. T\n-00005740: 6865 2072 6f74 6174 6520 7472 616e 7366 he rotate transf\n-00005750: 6f72 6d20 7475 726e 7320 7468 6520 7465 orm turns the te\n-00005760: 7472 6168 6564 726f 6e0a 3930 2064 6567 trahedron.90 deg\n-00005770: 7265 6573 2061 626f 7574 2074 6865 206f rees about the o\n-00005780: 7269 6769 6e2e 2020 5468 6520 6178 6973 rigin. The axis\n-00005790: 206f 6620 726f 7461 7469 6f6e 2069 7320 of rotation is \n-000057a0: 7468 6520 7665 6374 6f72 0a5b 312c 302c the vector.[1,0,\n-000057b0: 305d 2e20 2042 7920 7468 6520 e280 9c72 0]. By the ...r\n-000057c0: 6967 6874 2068 616e 6420 7275 6c65 e280 ight hand rule..\n-000057d0: 9d2c 2074 6869 7320 6361 7573 6573 2074 ., this causes t\n-000057e0: 6865 2074 6f70 206f 6620 7468 650a 7465 he top of the.te\n-000057f0: 7472 6168 6564 726f 6e20 746f 2072 6f74 trahedron to rot\n-00005800: 6174 6520 746f 7761 7264 2074 6865 2076 ate toward the v\n-00005810: 6965 7765 7220 616e 6420 7468 6520 626f iewer and the bo\n-00005820: 7474 6f6d 2061 7761 792e 2020 5468 6520 ttom away. The \n-00005830: 7275 6c65 0a72 6563 6569 7665 7320 6974 rule.receives it\n-00005840: 7320 6e61 6d65 2066 726f 6d20 7468 6520 s name from the \n-00005850: 666f 6c6c 6f77 696e 6720 6465 6669 6e69 following defini\n-00005860: 7469 6f6e 3a0a 2020 2020 202a 5269 6768 tion:. *Righ\n-00005870: 7420 6861 6e64 2072 756c 652e 2a20 2049 t hand rule.* I\n-00005880: 6620 7468 6520 7269 6768 7420 6861 6e64 f the right hand\n-00005890: 2069 7320 7772 6170 7065 6420 6172 6f75 is wrapped arou\n-000058a0: 6e64 2061 6e79 2061 7869 730a 2020 2020 nd any axis. \n-000058b0: 2077 6974 6820 7468 6520 7468 756d 6220 with the thumb \n-000058c0: 706f 696e 7469 6e67 2069 6e20 7468 6520 pointing in the \n-000058d0: 6178 6973 2064 6972 6563 7469 6f6e 2c20 axis direction, \n-000058e0: 7468 656e 2074 6865 2066 696e 6765 7273 then the fingers\n-000058f0: 0a20 2020 2020 6375 726c 2069 6e20 7468 . curl in th\n-00005900: 6520 6469 7265 6374 696f 6e20 6f66 2070 e direction of p\n-00005910: 6f73 6974 6976 6520 726f 7461 7469 6f6e ositive rotation\n-00005920: 2061 626f 7574 2074 6861 7420 6178 6973 about that axis\n-00005930: 2e0a 2020 2054 6865 2074 7261 6e73 6c61 .. The transla\n-00005940: 7465 2074 7261 6e73 666f 726d 206d 6f76 te transform mov\n-00005950: 6573 2074 6865 2070 7972 616d 6964 206c es the pyramid l\n-00005960: 6174 6572 616c 6c79 2074 6f20 7468 6520 aterally to the \n-00005970: 7269 6768 7420 6279 0a61 6464 696e 6720 right by.adding \n-00005980: 7468 6520 7665 6374 6f72 205b 322e 352c the vector [2.5,\n-00005990: 302c 305d 2074 6f20 6561 6368 2076 6572 0,0] to each ver\n-000059a0: 7465 7820 636f 6f72 6469 6e61 7465 2e20 tex coordinate. \n-000059b0: 2054 6865 2072 6573 756c 7420 6973 0a73 The result is.s\n-000059c0: 686f 776e 2068 6572 652e 0a0a 0008 5b69 hown here.....[i\n-000059d0: 6d61 6765 2073 7263 3d22 6578 3035 302e mage src=\"ex050.\n-000059e0: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n-000059f0: 2065 7830 3530 206f 6d69 7474 6564 2069 ex050 omitted i\n-00005a00: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n-00005a10: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n-00005a20: 2200 085d 0a0a 1f0a 4669 6c65 3a20 736b \"..]....File: sk\n-00005a30: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-00005a40: 3a20 5265 7065 6174 6564 206f 626a 6563 : Repeated objec\n-00005a50: 7473 2c20 204e 6578 743a 2053 7765 7074 ts, Next: Swept\n-00005a60: 206f 626a 6563 7473 2c20 2050 7265 763a objects, Prev:\n-00005a70: 204f 626a 6563 7420 7472 616e 7366 6f72 Object transfor\n-00005a80: 6d73 2c20 2055 703a 2049 6e74 726f 6475 ms, Up: Introdu\n-00005a90: 6374 696f 6e20 6279 2065 7861 6d70 6c65 ction by example\n-00005aa0: 0a0a 322e 3620 5265 7065 6174 6564 206f ..2.6 Repeated o\n-00005ab0: 626a 6563 7473 0a3d 3d3d 3d3d 3d3d 3d3d bjects.=========\n-00005ac0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0a54 6f20 ===========..To \n-00005ad0: 6472 6177 2073 6576 656e 2069 6e73 7461 draw seven insta\n-00005ae0: 6e63 6573 206f 6620 7468 6520 7465 7472 nces of the tetr\n-00005af0: 6168 6564 726f 6e2c 2065 6163 6820 6469 ahedron, each di\n-00005b00: 6666 6572 696e 6720 6672 6f6d 2074 6865 ffering from the\n-00005b10: 206c 6173 740a 6279 2074 6865 2073 616d last.by the sam\n-00005b20: 6520 7472 616e 7366 6f72 6d2c 2072 6570 e transform, rep\n-00005b30: 6c61 6365 2074 6865 206c 6173 7420 7477 lace the last tw\n-00005b40: 6f20 636f 6d6d 616e 6473 206f 6620 7468 o commands of th\n-00005b50: 6520 7072 6576 696f 7573 0a65 7861 6d70 e previous.examp\n-00005b60: 6c65 2077 6974 680a 2020 7265 7065 6174 le with. repeat\n-00005b70: 207b 2037 2c20 726f 7461 7465 2831 352c { 7, rotate(15,\n-00005b80: 2028 302c 302c 3029 2c20 5b31 2c30 2c30 (0,0,0), [1,0,0\n-00005b90: 5d29 2025 2063 6f70 7920 696e 206e 6577 ]) % copy in new\n-00005ba0: 2070 6f73 6974 696f 6e0a 2020 2020 2020 position. \n-00005bb0: 2020 2020 2020 2020 7468 656e 2074 7261 then tra\n-00005bc0: 6e73 6c61 7465 285b 322c 302c 305d 2920 nslate([2,0,0]) \n-00005bd0: 7d20 7b70 6965 7263 6564 5f74 6574 7261 } {pierced_tetra\n-00005be0: 6865 6472 6f6e 7d0a 416e 6420 7468 6520 hedron}.And the \n-00005bf0: 7265 7375 6c74 2e2e 2e0a 0a00 085b 696d result.......[im\n-00005c00: 6167 6520 7372 633d 2265 7830 3630 2e70 age src=\"ex060.p\n-00005c10: 6e67 2220 7465 7874 3d22 496d 6167 6520 ng\" text=\"Image \n-00005c20: 6578 3036 3020 6f6d 6974 7465 6420 696e ex060 omitted in\n-00005c30: 2074 6578 7420 7665 7273 696f 6e20 6f66 text version of\n-00005c40: 2074 6869 7320 646f 6375 6d65 6e74 2e22 this document.\"\n-00005c50: 0008 5d0a 0a1f 0a46 696c 653a 2073 6b65 ..]....File: ske\n-00005c60: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n-00005c70: 2053 7765 7074 206f 626a 6563 7473 2c20 Swept objects, \n-00005c80: 2050 7265 763a 2052 6570 6561 7465 6420 Prev: Repeated \n-00005c90: 6f62 6a65 6374 732c 2020 5570 3a20 496e objects, Up: In\n-00005ca0: 7472 6f64 7563 7469 6f6e 2062 7920 6578 troduction by ex\n-00005cb0: 616d 706c 650a 0a32 2e37 2053 7765 7074 ample..2.7 Swept\n-00005cc0: 206f 626a 6563 7473 0a3d 3d3d 3d3d 3d3d objects.=======\n-00005cd0: 3d3d 3d3d 3d3d 3d3d 3d3d 0a0a 4d61 6e79 ==========..Many\n-00005ce0: 2066 616d 696c 6961 7220 7368 6170 6573 familiar shapes\n-00005cf0: 2063 616e 2062 6520 6765 6e65 7261 7465 can be generate\n-00005d00: 6420 6279 2073 7765 6570 696e 6720 7369 d by sweeping si\n-00005d10: 6d70 6c65 7220 6f6e 6573 2074 6872 6f75 mpler ones throu\n-00005d20: 6768 0a73 7061 6365 2061 6e64 2063 6f6e gh.space and con\n-00005d30: 7369 6465 7269 6e67 2074 6865 2072 6573 sidering the res\n-00005d40: 756c 7469 6e67 2070 6174 682c 2073 7572 ulting path, sur\n-00005d50: 6661 6365 2c20 6f72 2076 6f6c 756d 652e face, or volume.\n-00005d60: 2020 e280 9853 6b65 7463 68e2 8099 0a69 ...Sketch....i\n-00005d70: 6d70 6c65 6d65 6e74 7320 7468 6973 2069 mplements this i\n-00005d80: 6465 6120 696e 2074 6865 2073 7765 6570 dea in the sweep\n-00005d90: 2063 6f6d 6d61 6e64 2e0a 2020 6465 6620 command.. def \n-00005da0: 6e5f 7365 6773 2038 0a20 2073 7765 6570 n_segs 8. sweep\n-00005db0: 207b 206e 5f73 6567 732c 2072 6f74 6174 { n_segs, rotat\n-00005dc0: 6528 3138 3020 2f20 6e5f 7365 6773 2c20 e(180 / n_segs, \n-00005dd0: 2830 2c30 2c30 292c 205b 302c 302c 315d (0,0,0), [0,0,1]\n-00005de0: 2920 7d20 2831 2c30 2c30 290a 5468 6973 ) } (1,0,0).This\n-00005df0: 2063 6f64 6520 7377 6565 7073 2074 6865 code sweeps the\n-00005e00: 2070 6f69 6e74 2028 312c 302c 3029 2065 point (1,0,0) e\n-00005e10: 6967 6874 2074 696d 6573 2062 7920 726f ight times by ro\n-00005e20: 7461 7469 6e67 2069 7420 3138 302f 3820 tating it 180/8 \n-00005e30: 3d0a 3232 2e35 2064 6567 7265 6573 2065 =.22.5 degrees e\n-00005e40: 6163 6820 7469 6d65 2061 6e64 2063 6f6e ach time and con\n-00005e50: 6e65 6374 696e 6720 7468 6520 7265 7375 necting the resu\n-00005e60: 6c74 696e 6720 706f 696e 7473 2077 6974 lting points wit\n-00005e70: 6820 6c69 6e65 0a73 6567 6d65 6e74 732e h line.segments.\n-00005e80: 2020 5468 6520 6465 6620 7573 6564 2068 The def used h\n-00005e90: 6572 6520 6973 2061 20e2 809c 7363 616c ere is a ...scal\n-00005ea0: 6172 e280 9d20 6465 6669 6e69 7469 6f6e ar... definition\n-00005eb0: 2e20 2052 6566 6572 656e 6365 7320 746f . References to\n-00005ec0: 0a73 6361 6c61 7273 2068 6176 6520 6e6f .scalars have no\n-00005ed0: 2065 6e63 6c6f 7369 6e67 2062 7261 636b enclosing brack\n-00005ee0: 6574 7320 6174 2061 6c6c 2e0a 0a2a 204d ets at all...* M\n-00005ef0: 656e 753a 0a0a 2a20 506f 696e 7420 7377 enu:..* Point sw\n-00005f00: 6565 7073 3a3a 2020 2020 2020 2020 2020 eeps:: \n-00005f10: 2020 2020 2020 5377 6570 7420 706f 696e Swept poin\n-00005f20: 7473 206d 616b 6520 6c69 6e65 7320 616e ts make lines an\n-00005f30: 6420 706f 6c79 676f 6e73 2e0a 2a20 506f d polygons..* Po\n-00005f40: 6c79 6c69 6e65 2073 7765 6570 733a 3a20 lyline sweeps:: \n-00005f50: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n-00005f60: 7420 6c69 6e65 7320 6d61 6b65 2073 7572 t lines make sur\n-00005f70: 6661 6365 732e 0a2a 204e 6573 7465 6420 faces..* Nested \n-00005f80: 7377 6565 7073 3a3a 2020 2020 2020 2020 sweeps:: \n-00005f90: 2020 2020 2020 2053 7765 7074 2073 7765 Swept swe\n-00005fa0: 6570 7320 6172 6520 7573 6566 756c 210a eps are useful!.\n-00005fb0: 2a20 506f 6c79 676f 6e20 7377 6565 7073 * Polygon sweeps\n-00005fc0: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n-00005fd0: 5377 6570 7420 706f 6c79 676f 6e73 206d Swept polygons m\n-00005fe0: 616b 6520 736f 6c69 6473 2e2e 2e0a 2a20 ake solids....* \n-00005ff0: 506f 6c79 6c69 6e65 2073 7765 6570 7320 Polyline sweeps \n-00006000: 7769 7468 2063 6c6f 7375 7265 3a3a 2020 with closure:: \n-00006010: 616e 6420 736f 2064 6f20 636c 6f73 6564 and so do closed\n-00006020: 2070 6f6c 796c 696e 6520 7377 6565 7073 polyline sweeps\n-00006030: 2e0a 2a20 4166 6669 6e65 2061 7269 7468 ..* Affine arith\n-00006040: 6d65 7469 633a 3a20 2020 2020 2020 2020 metic:: \n-00006050: 2020 536b 6574 6368 2075 7365 6675 6c20 Sketch useful \n-00006060: 6d61 7468 2065 7870 7265 7373 696f 6e2e math expression.\n-00006070: 0a2a 204d 6f72 6520 746f 206c 6561 726e .* More to learn\n-00006080: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n-00006090: 2043 6865 636b 206f 7574 2074 6865 204d Check out the M\n-000060a0: 6f62 6975 7320 7374 7269 7021 0a0a 1f0a obius strip!....\n-000060b0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n-000060c0: 6f2c 2020 4e6f 6465 3a20 506f 696e 7420 o, Node: Point \n-000060d0: 7377 6565 7073 2c20 204e 6578 743a 2050 sweeps, Next: P\n-000060e0: 6f6c 796c 696e 6520 7377 6565 7073 2c20 olyline sweeps, \n-000060f0: 2050 7265 763a 2053 7765 7074 206f 626a Prev: Swept obj\n-00006100: 6563 7473 2c20 2055 703a 2053 7765 7074 ects, Up: Swept\n-00006110: 206f 626a 6563 7473 0a0a 322e 372e 3120 objects..2.7.1 \n-00006120: 506f 696e 7420 7377 6565 7073 0a2d 2d2d Point sweeps.---\n-00006130: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ---------------.\n-00006140: 0a53 7765 6570 696e 6720 6120 706f 696e .Sweeping a poin\n-00006150: 7420 6d61 6b65 7320 6120 6f6e 652d 6469 t makes a one-di\n-00006160: 6d65 6e73 696f 6e61 6c20 7061 7468 2c20 mensional path, \n-00006170: 7768 6963 6820 6973 2061 2070 6f6c 796c which is a polyl\n-00006180: 696e 652e 0a53 696e 6365 2077 6520 6861 ine..Since we ha\n-00006190: 7665 2073 7765 7074 2077 6974 6820 6120 ve swept with a \n-000061a0: 726f 7461 7469 6f6e 2c20 7468 6520 7265 rotation, the re\n-000061b0: 7375 6c74 2069 7320 6120 6369 7263 756c sult is a circul\n-000061c0: 6172 2061 7263 2e20 2048 6572 650a 6973 ar arc. Here.is\n-000061d0: 2077 6861 7420 6974 206c 6f6f 6b73 206c what it looks l\n-000061e0: 696b 652e 0a0a 0008 5b69 6d61 6765 2073 ike.....[image s\n-000061f0: 7263 3d22 6578 3037 302e 706e 6722 2074 rc=\"ex070.png\" t\n-00006200: 6578 743d 2249 6d61 6765 2065 7830 3730 ext=\"Image ex070\n-00006210: 206f 6d69 7474 6564 2069 6e20 7465 7874 omitted in text\n-00006220: 2076 6572 7369 6f6e 206f 6620 7468 6973 version of this\n-00006230: 2064 6f63 756d 656e 742e 2200 085d 0a0a document.\"..]..\n-00006240: 2020 2054 6869 7320 6973 2074 6865 2066 This is the f\n-00006250: 6972 7374 2065 7861 6d70 6c65 2077 6520 irst example we \n-00006260: 6861 7665 2073 6565 6e20 6f66 20e2 8098 have seen of ...\n-00006270: 736b 6574 6368 e280 9920 6172 6974 686d sketch... arithm\n-00006280: 6574 6963 2e20 2054 6865 0a65 7870 7265 etic. The.expre\n-00006290: 7373 696f 6e20 3138 3020 2f20 6e5f 7365 ssion 180 / n_se\n-000062a0: 6773 2063 6175 7365 7320 7468 6520 6569 gs causes the ei\n-000062b0: 6768 7420 726f 7461 7469 6f6e 7320 746f ght rotations to\n-000062c0: 2061 6464 2074 6f20 3138 302e 2020 4966 add to 180. If\n-000062d0: 0a79 6f75 2772 6520 7061 7969 6e67 2061 .you're paying a\n-000062e0: 7474 656e 7469 6f6e 2c20 796f 7527 6c6c ttention, you'll\n-000062f0: 2068 6176 6520 616c 7265 6164 7920 6e6f have already no\n-00006300: 7465 6420 7468 6174 2074 6865 7265 2061 ted that there a\n-00006310: 7265 205f 6e69 6e65 5f0a 706f 696e 7473 re _nine_.points\n-00006320: 2c20 7072 6f64 7563 696e 6720 6569 6768 , producing eigh\n-00006330: 7420 6c69 6e65 2073 6567 6d65 6e74 732e t line segments.\n-00006340: 0a0a 2020 2059 6f75 2063 616e 2063 6175 .. You can cau\n-00006350: 7365 2074 6865 2073 7765 7074 2070 6f69 se the swept poi\n-00006360: 6e74 2074 6f20 6765 6e65 7261 7465 2061 nt to generate a\n-00006370: 2073 696e 676c 6520 706f 6c79 676f 6e20 single polygon \n-00006380: 7261 7468 6572 0a74 6861 6e20 6120 706f rather.than a po\n-00006390: 6c79 6c69 6e65 2062 7920 7573 696e 6720 lyline by using \n-000063a0: 7468 6520 e280 9c63 6c6f 7375 7265 2074 the ...closure t\n-000063b0: 6167 e280 9d20 3c3e 2061 6674 6572 2074 ag... <> after t\n-000063c0: 6865 206e 756d 6265 7220 6f66 2073 7765 he number of swe\n-000063d0: 7074 0a6f 626a 6563 7473 2e20 2043 6f64 pt.objects. Cod\n-000063e0: 6520 616e 6420 7265 7375 6c74 2066 6f6c e and result fol\n-000063f0: 6c6f 770a 2020 6465 6620 6e5f 7365 6773 low. def n_segs\n-00006400: 2038 0a20 2073 7765 6570 207b 206e 5f73 8. sweep { n_s\n-00006410: 6567 733c 3e2c 2072 6f74 6174 6528 3138 egs<>, rotate(18\n-00006420: 3020 2f20 6e5f 7365 6773 2c20 2830 2c30 0 / n_segs, (0,0\n-00006430: 2c30 292c 205b 302c 302c 315d 2920 7d20 ,0), [0,0,1]) } \n-00006440: 2831 2c30 2c30 290a 0008 5b69 6d61 6765 (1,0,0)...[image\n-00006450: 2073 7263 3d22 6578 3038 302e 706e 6722 src=\"ex080.png\"\n-00006460: 2074 6578 743d 2249 6d61 6765 2065 7830 text=\"Image ex0\n-00006470: 3830 206f 6d69 7474 6564 2069 6e20 7465 80 omitted in te\n-00006480: 7874 2076 6572 7369 6f6e 206f 6620 7468 xt version of th\n-00006490: 6973 2064 6f63 756d 656e 742e 2200 085d is document.\"..]\n-000064a0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-000064b0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 506f .info, Node: Po\n-000064c0: 6c79 6c69 6e65 2073 7765 6570 732c 2020 lyline sweeps, \n-000064d0: 4e65 7874 3a20 4e65 7374 6564 2073 7765 Next: Nested swe\n-000064e0: 6570 732c 2020 5072 6576 3a20 506f 696e eps, Prev: Poin\n-000064f0: 7420 7377 6565 7073 2c20 2055 703a 2053 t sweeps, Up: S\n-00006500: 7765 7074 206f 626a 6563 7473 0a0a 322e wept objects..2.\n-00006510: 372e 3220 506f 6c79 6c69 6e65 2073 7765 7.2 Polyline swe\n-00006520: 6570 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d eps.------------\n-00006530: 2d2d 2d2d 2d2d 2d2d 2d0a 0a53 7765 6570 ---------..Sweep\n-00006540: 696e 6720 6120 706f 6c79 6c69 6e65 2070 ing a polyline p\n-00006550: 726f 6475 6365 7320 6120 7375 7266 6163 roduces a surfac\n-00006560: 6520 636f 6d70 6f73 6564 206f 6620 6d61 e composed of ma\n-00006570: 6e79 2066 6163 6573 2e20 2054 6865 0a75 ny faces. The.u\n-00006580: 6e62 726f 6b65 6e20 6865 6c69 7820 696e nbroken helix in\n-00006590: 2074 6865 2065 7861 6d70 6c65 202a 6e6f the example *no\n-000065a0: 7465 2048 656c 6978 2077 6974 6820 6375 te Helix with cu\n-000065b0: 6c6c 2073 6574 2066 616c 7365 2074 6865 ll set false the\n-000065c0: 6e0a 7472 7565 3a3a 2069 7320 7072 6f64 n.true:: is prod\n-000065d0: 7563 6564 2062 7920 7468 6973 2063 6f64 uced by this cod\n-000065e0: 6520 2870 6c75 7320 6120 7375 7272 6f75 e (plus a surrou\n-000065f0: 6e64 696e 6720 7075 7420 726f 7461 7469 nding put rotati\n-00006600: 6f6e 2074 6f20 6d61 6b65 0a61 6e20 696e on to make.an in\n-00006610: 7465 7265 7374 696e 6720 7669 6577 3b20 teresting view; \n-00006620: 7468 6973 2068 6173 2062 6565 6e20 6f6d this has been om\n-00006630: 6974 7465 6429 2e0a 2020 6465 6620 4b20 itted).. def K \n-00006640: 5b30 2c30 2c31 5d0a 2020 7377 6565 705b [0,0,1]. sweep[\n-00006650: 6375 6c6c 3d66 616c 7365 5d20 7b0a 2020 cull=false] {. \n-00006660: 2020 3630 2c20 0a20 2020 2072 6f74 6174 60, . rotat\n-00006670: 6528 3130 2c20 2830 2c30 2c30 292c 205b e(10, (0,0,0), [\n-00006680: 4b5d 2920 7468 656e 2074 7261 6e73 6c61 K]) then transla\n-00006690: 7465 2831 2f36 202a 205b 4b5d 2920 0a20 te(1/6 * [K]) . \n-000066a0: 207d 206c 696e 655b 6c69 6e65 7769 6474 } line[linewidt\n-000066b0: 683d 3270 745d 282d 312c 3029 2831 2c30 h=2pt](-1,0)(1,0\n-000066c0: 290a 4167 6169 6e2c 2036 3020 7365 676d ).Again, 60 segm\n-000066d0: 656e 7473 206f 6620 7468 6520 6865 6c69 ents of the heli\n-000066e0: 7820 6172 6520 7072 6f64 7563 6564 2062 x are produced b\n-000066f0: 7920 636f 6e6e 6563 7469 6e67 2036 3120 y connecting 61 \n-00006700: 696e 7374 616e 6365 730a 6f66 2074 6865 instances.of the\n-00006710: 2073 7765 7074 206c 696e 652e 2020 4f70 swept line. Op\n-00006720: 7469 6f6e 7320 6170 706c 6965 6420 746f tions applied to\n-00006730: 2074 6865 2073 7765 6570 2c20 6865 7265 the sweep, here\n-00006740: 2063 756c 6c3d 6661 6c73 652c 2061 7265 cull=false, are\n-00006750: 0a74 7265 6174 6564 2061 7320 6f70 7469 .treated as opti\n-00006760: 6f6e 7320 666f 7220 7468 6520 6765 6e65 ons for the gene\n-00006770: 7261 7465 6420 706f 6c79 676f 6e20 6f72 rated polygon or\n-00006780: 2070 6f6c 796c 696e 652e 2020 4f70 7469 polyline. Opti\n-00006790: 6f6e 7320 6f66 0a74 6865 2073 7765 7074 ons of.the swept\n-000067a0: 206c 696e 6520 6974 7365 6c66 2c20 6865 line itself, he\n-000067b0: 7265 206c 696e 6577 6964 7468 3d32 7074 re linewidth=2pt\n-000067c0: 2c20 6172 6520 6967 6e6f 7265 642c 2074 , are ignored, t\n-000067d0: 686f 7567 6820 7769 7468 2061 0a77 6172 hough with a.war\n-000067e0: 6e69 6e67 2e20 2054 6869 7320 6465 6620 ning. This def \n-000067f0: 6973 2061 20e2 809c 7665 6374 6f72 e280 is a ...vector..\n-00006800: 9d20 6465 6669 6e69 7469 6f6e 2c20 7768 . definition, wh\n-00006810: 6963 6820 6d75 7374 2062 6520 7265 6665 ich must be refe\n-00006820: 7265 6e63 6564 0a77 6974 6820 7371 7561 renced.with squa\n-00006830: 7265 2062 7261 636b 6574 732c 2065 2e67 re brackets, e.g\n-00006840: 2e20 5b66 6f6f 5d2e 0a0a 1f0a 4669 6c65 . [foo].....File\n-00006850: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-00006860: 4e6f 6465 3a20 4e65 7374 6564 2073 7765 Node: Nested swe\n-00006870: 6570 732c 2020 4e65 7874 3a20 506f 6c79 eps, Next: Poly\n-00006880: 676f 6e20 7377 6565 7073 2c20 2050 7265 gon sweeps, Pre\n-00006890: 763a 2050 6f6c 796c 696e 6520 7377 6565 v: Polyline swee\n-000068a0: 7073 2c20 2055 703a 2053 7765 7074 206f ps, Up: Swept o\n-000068b0: 626a 6563 7473 0a0a 322e 372e 3320 4e65 bjects..2.7.3 Ne\n-000068c0: 7374 6564 2073 7765 6570 730a 2d2d 2d2d sted sweeps.----\n-000068d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ---------------.\n-000068e0: 0a57 6865 6e20 7468 6520 6365 6e74 6572 .When the center\n-000068f0: 2070 6f69 6e74 206f 6620 726f 7461 7469 point of rotati\n-00006900: 6f6e 2069 7320 6f6d 6974 7465 642c 2074 on is omitted, t\n-00006910: 6865 206f 7269 6769 6e20 6973 2061 7373 he origin is ass\n-00006920: 756d 6564 2e0a 5768 656e 2061 2070 6f69 umed..When a poi\n-00006930: 6e74 2068 6173 206f 6e6c 7920 7477 6f20 nt has only two \n-00006940: 636f 6f72 6469 6e61 7465 732c 2074 6865 coordinates, the\n-00006950: 7920 6172 6520 7461 6b65 6e20 6173 2078 y are taken as x\n-00006960: 2061 6e64 2079 2c20 7769 7468 0a7a 3d30 and y, with.z=0\n-00006970: 2061 7373 756d 6564 2e20 2041 2074 6f72 assumed. A tor\n-00006980: 6f69 6420 6973 2074 6865 7265 666f 7265 oid is therefore\n-00006990: 206f 6274 6169 6e65 6420 7769 7468 2074 obtained with t\n-000069a0: 6869 7320 636f 6465 2e0a 2020 6465 6620 his code.. def \n-000069b0: 6e5f 746f 726f 6964 5f73 6567 7320 3230 n_toroid_segs 20\n-000069c0: 2020 2064 6566 206e 5f63 6972 636c 655f def n_circle_\n-000069d0: 7365 6773 2031 360a 2020 6465 6620 725f segs 16. def r_\n-000069e0: 6d69 6e6f 7220 3120 2020 2020 2020 2020 minor 1 \n-000069f0: 2064 6566 2072 5f6d 616a 6f72 2031 2e35 def r_major 1.5\n-00006a00: 0a20 2073 7765 6570 207b 206e 5f74 6f72 . sweep { n_tor\n-00006a10: 6f69 645f 7365 6773 2c20 726f 7461 7465 oid_segs, rotate\n-00006a20: 2833 3630 202f 206e 5f74 6f72 6f69 645f (360 / n_toroid_\n-00006a30: 7365 6773 2c20 5b30 2c31 2c30 5d29 207d segs, [0,1,0]) }\n-00006a40: 0a20 2020 2073 7765 6570 207b 206e 5f63 . sweep { n_c\n-00006a50: 6972 636c 655f 7365 6773 2c20 726f 7461 ircle_segs, rota\n-00006a60: 7465 2833 3630 202f 206e 5f63 6972 636c te(360 / n_circl\n-00006a70: 655f 7365 6773 2c20 2872 5f6d 616a 6f72 e_segs, (r_major\n-00006a80: 2c30 2c30 2929 207d 200a 2020 2020 2020 ,0,0)) } . \n-00006a90: 2872 5f6d 616a 6f72 202b 2072 5f6d 696e (r_major + r_min\n-00006aa0: 6f72 2c20 3029 0a20 2020 466f 7220 696e or, 0). For in\n-00006ab0: 7475 6974 696f 6e2c 2074 6865 2069 6465 tuition, the ide\n-00006ac0: 6120 6f66 2074 6865 2063 6f64 6520 6973 a of the code is\n-00006ad0: 2074 6f20 736b 6574 6368 2061 2063 6972 to sketch a cir\n-00006ae0: 636c 6520 746f 2074 6865 0a72 6967 6874 cle to the.right\n-00006af0: 206f 6620 7468 6520 6f72 6967 696e 2069 of the origin i\n-00006b00: 6e20 7468 6520 7879 2d70 6c61 6e65 2c20 n the xy-plane, \n-00006b10: 7468 656e 2072 6f74 6174 6520 7468 6174 then rotate that\n-00006b20: 2063 6972 636c 6520 226f 7574 206f 6620 circle \"out of \n-00006b30: 7468 650a 706c 616e 6522 2061 626f 7574 the.plane\" about\n-00006b40: 2074 6865 2079 2d61 7869 7320 746f 206d the y-axis to m\n-00006b50: 616b 6520 7468 6520 6669 6e61 6c20 6669 ake the final fi\n-00006b60: 6775 7265 2e20 2054 6869 7320 7072 6f64 gure. This prod\n-00006b70: 7563 6573 2074 6865 0a66 6f6c 6c6f 7769 uces the.followi\n-00006b80: 6e67 2e20 2028 4120 7669 6577 2072 6f74 ng. (A view rot\n-00006b90: 6174 696f 6e20 616e 6420 736f 6d65 2061 ation and some a\n-00006ba0: 7865 7320 6861 7665 2062 6565 6e20 6164 xes have been ad\n-00006bb0: 6465 642e 290a 0a00 085b 696d 6167 6520 ded.)....[image \n-00006bc0: 7372 633d 2265 7830 3930 2e70 6e67 2220 src=\"ex090.png\" \n-00006bd0: 7465 7874 3d22 496d 6167 6520 6578 3039 text=\"Image ex09\n-00006be0: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n-00006bf0: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n-00006c00: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n-00006c10: 0a20 2020 5468 6973 2065 7861 6d70 6c65 . This example\n-00006c20: 2061 6c73 6f20 7368 6f77 7320 7468 6174 also shows that\n-00006c30: 2074 6865 2073 7765 7074 206f 626a 6563 the swept objec\n-00006c40: 7420 6d61 7920 6974 7365 6c66 2062 6520 t may itself be \n-00006c50: 616e 6f74 6865 720a e280 9873 7765 6570 another....sweep\n-00006c60: e280 992e 2020 496e 2066 6163 742c 2069 .... In fact, i\n-00006c70: 7420 6d61 7920 6265 205f 616e 795f 20e2 t may be _any_ .\n-00006c80: 8098 736b 6574 6368 e280 9920 6578 7072 ..sketch... expr\n-00006c90: 6573 7369 6f6e 2074 6861 7420 7265 7375 ession that resu\n-00006ca0: 6c74 7320 696e 2061 0a6c 6973 7420 6f66 lts in a.list of\n-00006cb0: 206f 6e65 206f 7220 6d6f 7265 2070 6f69 one or more poi\n-00006cc0: 6e74 7320 6f72 2c20 616c 7465 726e 6174 nts or, alternat\n-00006cd0: 656c 792c 2061 206c 6973 7420 6f66 206f ely, a list of o\n-00006ce0: 6e65 206f 7220 6d6f 7265 0a70 6f6c 796c ne or more.polyl\n-00006cf0: 696e 6573 2061 6e64 2070 6f6c 7967 6f6e ines and polygon\n-00006d00: 732e 2020 5468 6520 6c61 7474 6572 206b s. The latter k\n-00006d10: 696e 6420 6f66 206c 6973 7420 6361 6e20 ind of list can \n-00006d20: 6265 2063 7265 6174 6564 2077 6974 6820 be created with \n-00006d30: 610a 7b20 7d2d 656e 636c 6f73 6564 2062 a.{ }-enclosed b\n-00006d40: 6c6f 636b 2c20 7065 7268 6170 7320 666f lock, perhaps fo\n-00006d50: 6c6c 6f77 696e 6720 6120 7075 7420 6f72 llowing a put or\n-00006d60: 2072 6570 6561 742e 0a0a 1f0a 4669 6c65 repeat.....File\n-00006d70: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-00006d80: 4e6f 6465 3a20 506f 6c79 676f 6e20 7377 Node: Polygon sw\n-00006d90: 6565 7073 2c20 204e 6578 743a 2050 6f6c eeps, Next: Pol\n-00006da0: 796c 696e 6520 7377 6565 7073 2077 6974 yline sweeps wit\n-00006db0: 6820 636c 6f73 7572 652c 2020 5072 6576 h closure, Prev\n-00006dc0: 3a20 4e65 7374 6564 2073 7765 6570 732c : Nested sweeps,\n-00006dd0: 2020 5570 3a20 5377 6570 7420 6f62 6a65 Up: Swept obje\n-00006de0: 6374 730a 0a32 2e37 2e34 2050 6f6c 7967 cts..2.7.4 Polyg\n-00006df0: 6f6e 2073 7765 6570 730a 2d2d 2d2d 2d2d on sweeps.------\n-00006e00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a --------------..\n-00006e10: 5377 6565 7069 6e67 2061 2070 6f6c 7967 Sweeping a polyg\n-00006e20: 6f6e 2063 7265 6174 6573 2061 2063 6c6f on creates a clo\n-00006e30: 7365 6420 7375 7266 6163 6520 7769 7468 sed surface with\n-00006e40: 2070 6f6c 7967 6f6e 7320 6174 2074 6865 polygons at the\n-00006e50: 2065 6e64 732c 0a77 6869 6368 2061 7265 ends,.which are\n-00006e60: 206a 7573 7420 636f 7069 6573 206f 6620 just copies of \n-00006e70: 7468 6520 6f72 6967 696e 616c 2c20 6170 the original, ap\n-00006e80: 7072 6f70 7269 6174 656c 7920 706f 7369 propriately posi\n-00006e90: 7469 6f6e 6564 2e20 202a 4e6f 7465 0a53 tioned. *Note.S\n-00006ea0: 6f6c 6964 2063 6f69 6c20 6578 616d 706c olid coil exampl\n-00006eb0: 653a 3a2e 2020 4f70 7469 6f6e 7320 6f6e e::. Options on\n-00006ec0: 2074 6865 2073 7765 7074 2070 6f6c 7967 the swept polyg\n-00006ed0: 6f6e 2c20 6966 2074 6865 7920 6578 6973 on, if they exis\n-00006ee0: 742c 2061 7265 0a61 7070 6c69 6564 2074 t, are.applied t\n-00006ef0: 6f20 7468 6520 656e 6473 2e20 204f 7468 o the ends. Oth\n-00006f00: 6572 7769 7365 2074 6865 2073 7765 6570 erwise the sweep\n-00006f10: 206f 7074 696f 6e73 2061 7265 2075 7365 options are use\n-00006f20: 6420 7468 726f 7567 686f 7574 2e0a 0a1f d throughout....\n-00006f30: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-00006f40: 666f 2c20 204e 6f64 653a 2050 6f6c 796c fo, Node: Polyl\n-00006f50: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n-00006f60: 636c 6f73 7572 652c 2020 4e65 7874 3a20 closure, Next: \n-00006f70: 4166 6669 6e65 2061 7269 7468 6d65 7469 Affine arithmeti\n-00006f80: 632c 2020 5072 6576 3a20 506f 6c79 676f c, Prev: Polygo\n-00006f90: 6e20 7377 6565 7073 2c20 2055 703a 2053 n sweeps, Up: S\n-00006fa0: 7765 7074 206f 626a 6563 7473 0a0a 322e wept objects..2.\n-00006fb0: 372e 3520 506f 6c79 6c69 6e65 2073 7765 7.5 Polyline swe\n-00006fc0: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n-00006fd0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n+00005280: 2520 6c65 6674 0a20 2020 2070 6f6c 7967 % left. polyg\n+00005290: 6f6e 5b66 696c 6c63 6f6c 6f72 3d6c 6967 on[fillcolor=lig\n+000052a0: 6874 6772 6179 5d28 7033 2928 7032 2928 htgray](p3)(p2)(\n+000052b0: 7034 2920 2520 7265 6172 0a20 2020 206c p4) % rear. l\n+000052c0: 696e 655b 6c69 6e65 636f 6c6f 723d 7265 ine[linecolor=re\n+000052d0: 645d 282d 312c 2d31 2c2d 3129 2832 2c32 d](-1,-1,-1)(2,2\n+000052e0: 2c32 290a 2020 7d0a 2020 7b70 6965 7263 ,2). }. {pierc\n+000052f0: 6564 5f74 6574 7261 6865 6472 6f6e 7d20 ed_tetrahedron} \n+00005300: 2025 2074 6574 7261 6865 6472 6f6e 2069 % tetrahedron i\n+00005310: 6e20 6f72 6967 696e 616c 2070 6f73 6974 n original posit\n+00005320: 696f 6e0a 2020 7075 7420 7b20 726f 7461 ion. put { rota\n+00005330: 7465 2839 302c 2028 302c 302c 3029 2c20 te(90, (0,0,0), \n+00005340: 5b31 2c30 2c30 5d29 2025 2063 6f70 7920 [1,0,0]) % copy \n+00005350: 696e 206e 6577 2070 6f73 6974 696f 6e0a in new position.\n+00005360: 2020 2020 2020 2020 7468 656e 2074 7261 then tra\n+00005370: 6e73 6c61 7465 285b 322e 352c 302c 305d nslate([2.5,0,0]\n+00005380: 2920 7d20 7b70 6965 7263 6564 5f74 6574 ) } {pierced_tet\n+00005390: 7261 6865 6472 6f6e 7d0a 4865 7265 2074 rahedron}.Here t\n+000053a0: 6865 2065 6e74 6972 6520 636f 6465 206f he entire code o\n+000053b0: 6620 7468 6520 7072 6576 696f 7573 2065 f the previous e\n+000053c0: 7861 6d70 6c65 2068 6173 2062 6565 6e20 xample has been \n+000053d0: 7772 6170 7065 6420 696e 2061 0a64 6566 wrapped in a.def\n+000053e0: 696e 6974 696f 6e20 6279 2066 6f72 6d69 inition by formi\n+000053f0: 6e67 2061 20e2 809c 626c 6f63 6be2 809d ng a ...block...\n+00005400: 2077 6974 6820 6272 6163 6573 2028 6120 with braces (a \n+00005410: 7369 6e67 6c65 2069 7465 6d20 776f 756c single item woul\n+00005420: 6420 6e6f 740a 6e65 6564 2074 6865 6d29 d not.need them)\n+00005430: 2e20 2054 6865 2070 6f69 6e74 2064 6566 . The point def\n+00005440: 696e 6974 696f 6e73 206e 6573 7465 6420 initions nested \n+00005450: 696e 7369 6465 2074 6865 2062 7261 6365 inside the brace\n+00005460: 7320 6172 650a e280 9c6c 6578 6963 616c s are....lexical\n+00005470: 6c79 2073 636f 7065 64e2 809d 2e20 2054 ly scoped.... T\n+00005480: 6865 6972 206d 6561 6e69 6e67 2065 7874 heir meaning ext\n+00005490: 656e 6473 206f 6e6c 7920 746f 2074 6865 ends only to the\n+000054a0: 2065 6e64 206f 6620 7468 6520 626c 6f63 end of the bloc\n+000054b0: 6b2e 0a54 6865 206f 7574 6572 2064 6566 k..The outer def\n+000054c0: 2069 7320 6361 6c6c 6564 2061 20e2 809c is called a ...\n+000054d0: 6472 6177 6162 6c65 e280 9d20 6465 6669 drawable... defi\n+000054e0: 6e69 7469 6f6e 2062 6563 6175 7365 2069 nition because i\n+000054f0: 7420 6465 7363 7269 6265 730a 736f 6d65 t describes.some\n+00005500: 7468 696e 6720 7468 6174 2063 616e 2062 thing that can b\n+00005510: 6520 6472 6177 6e2e 0a0a 2020 2041 2064 e drawn... A d\n+00005520: 7261 7761 626c 6520 6465 6669 6e69 7469 rawable definiti\n+00005530: 6f6e 2062 7920 6974 7365 6c66 2063 6175 on by itself cau\n+00005540: 7365 7320 6e6f 7468 696e 6720 746f 2068 ses nothing to h\n+00005550: 6170 7065 6e20 756e 7469 6c20 6974 730a appen until its.\n+00005560: 6e61 6d65 2069 7320 7265 6665 7265 6e63 name is referenc\n+00005570: 6564 2e20 2044 7261 7761 626c 6520 7265 ed. Drawable re\n+00005580: 6665 7265 6e63 6573 206d 7573 7420 6265 ferences must be\n+00005590: 2065 6e63 6c6f 7365 6420 696e 2063 7572 enclosed in cur\n+000055a0: 6c79 0a62 7261 6365 732c 2065 2e67 2e20 ly.braces, e.g. \n+000055b0: 7b66 6f6f 7d2c 2077 6974 6820 6e6f 2069 {foo}, with no i\n+000055c0: 6e74 6572 7665 6e69 6e67 2077 6869 7465 ntervening white\n+000055d0: 2073 7061 6365 2e20 2049 6e20 7468 6520 space. In the \n+000055e0: 636f 6465 2061 626f 7665 2c0a 7468 6520 code above,.the \n+000055f0: 6669 7273 7420 7265 6665 7265 6e63 6520 first reference \n+00005600: 7b70 6965 7263 6564 5f74 6574 7261 6865 {pierced_tetrahe\n+00005610: 6472 6f6e 7d20 6973 2061 2070 6c61 696e dron} is a plain\n+00005620: 206f 6e65 2e20 2049 7473 2065 6666 6563 one. Its effec\n+00005630: 7420 6973 0a6d 6572 656c 7920 746f 2064 t is.merely to d\n+00005640: 7570 6c69 6361 7465 2074 6865 2065 6172 uplicate the ear\n+00005650: 6c69 6572 2064 7261 7769 6e67 2e20 2041 lier drawing. A\n+00005660: 6c6d 6f73 7420 616e 7920 7365 7269 6573 lmost any series\n+00005670: 206f 6620 e280 9873 6b65 7463 68e2 8099 of ...sketch...\n+00005680: 0a63 6f6d 6d61 6e64 7320 7374 7566 6620 .commands stuff \n+00005690: 6d61 7920 6265 2072 6570 6c61 6365 6420 may be replaced \n+000056a0: 7769 7468 2064 6566 2066 6f6f 207b 2073 with def foo { s\n+000056b0: 7475 6666 207d 207b 666f 6f7d 2077 6974 tuff } {foo} wit\n+000056c0: 686f 7574 0a63 6861 6e67 696e 6720 6974 hout.changing it\n+000056d0: 7320 6d65 616e 696e 672e 0a0a 2020 2054 s meaning... T\n+000056e0: 6865 2070 7574 2063 6f6d 6d61 6e64 2073 he put command s\n+000056f0: 7570 706c 6965 7320 6120 7365 636f 6e64 upplies a second\n+00005700: 2072 6566 6572 656e 6365 2c20 7468 6973 reference, this\n+00005710: 2074 696d 6520 7769 7468 2061 0ae2 809c time with a....\n+00005720: 7472 616e 7366 6f72 6de2 809d 2061 7070 transform... app\n+00005730: 6c69 6564 2066 6972 7374 2e20 2054 6865 lied first. The\n+00005740: 2072 6f74 6174 6520 7472 616e 7366 6f72 rotate transfor\n+00005750: 6d20 7475 726e 7320 7468 6520 7465 7472 m turns the tetr\n+00005760: 6168 6564 726f 6e0a 3930 2064 6567 7265 ahedron.90 degre\n+00005770: 6573 2061 626f 7574 2074 6865 206f 7269 es about the ori\n+00005780: 6769 6e2e 2020 5468 6520 6178 6973 206f gin. The axis o\n+00005790: 6620 726f 7461 7469 6f6e 2069 7320 7468 f rotation is th\n+000057a0: 6520 7665 6374 6f72 0a5b 312c 302c 305d e vector.[1,0,0]\n+000057b0: 2e20 2042 7920 7468 6520 e280 9c72 6967 . By the ...rig\n+000057c0: 6874 2068 616e 6420 7275 6c65 e280 9d2c ht hand rule...,\n+000057d0: 2074 6869 7320 6361 7573 6573 2074 6865 this causes the\n+000057e0: 2074 6f70 206f 6620 7468 650a 7465 7472 top of the.tetr\n+000057f0: 6168 6564 726f 6e20 746f 2072 6f74 6174 ahedron to rotat\n+00005800: 6520 746f 7761 7264 2074 6865 2076 6965 e toward the vie\n+00005810: 7765 7220 616e 6420 7468 6520 626f 7474 wer and the bott\n+00005820: 6f6d 2061 7761 792e 2020 5468 6520 7275 om away. 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T\n+000059b0: 6865 2072 6573 756c 7420 6973 0a73 686f he result is.sho\n+000059c0: 776e 2068 6572 652e 0a0a 0008 5b69 6d61 wn here.....[ima\n+000059d0: 6765 2073 7263 3d22 6578 3035 302e 706e ge src=\"ex050.pn\n+000059e0: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+000059f0: 7830 3530 206f 6d69 7474 6564 2069 6e20 x050 omitted in \n+00005a00: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+00005a10: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+00005a20: 085d 0a0a 1f0a 4669 6c65 3a20 736b 6574 .]....File: sket\n+00005a30: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+00005a40: 5265 7065 6174 6564 206f 626a 6563 7473 Repeated objects\n+00005a50: 2c20 204e 6578 743a 2053 7765 7074 206f , Next: Swept o\n+00005a60: 626a 6563 7473 2c20 2050 7265 763a 204f bjects, Prev: O\n+00005a70: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n+00005a80: 2c20 2055 703a 2049 6e74 726f 6475 6374 , Up: Introduct\n+00005a90: 696f 6e20 6279 2065 7861 6d70 6c65 0a0a ion by example..\n+00005aa0: 322e 3620 5265 7065 6174 6564 206f 626a 2.6 Repeated obj\n+00005ab0: 6563 7473 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d ects.===========\n+00005ac0: 3d3d 3d3d 3d3d 3d3d 3d0a 0a54 6f20 6472 =========..To dr\n+00005ad0: 6177 2073 6576 656e 2069 6e73 7461 6e63 aw seven instanc\n+00005ae0: 6573 206f 6620 7468 6520 7465 7472 6168 es of the tetrah\n+00005af0: 6564 726f 6e2c 2065 6163 6820 6469 6666 edron, each diff\n+00005b00: 6572 696e 6720 6672 6f6d 2074 6865 206c ering from the l\n+00005b10: 6173 740a 6279 2074 6865 2073 616d 6520 ast.by the same \n+00005b20: 7472 616e 7366 6f72 6d2c 2072 6570 6c61 transform, repla\n+00005b30: 6365 2074 6865 206c 6173 7420 7477 6f20 ce the last two \n+00005b40: 636f 6d6d 616e 6473 206f 6620 7468 6520 commands of the \n+00005b50: 7072 6576 696f 7573 0a65 7861 6d70 6c65 previous.example\n+00005b60: 2077 6974 680a 2020 7265 7065 6174 207b with. repeat {\n+00005b70: 2037 2c20 726f 7461 7465 2831 352c 2028 7, rotate(15, (\n+00005b80: 302c 302c 3029 2c20 5b31 2c30 2c30 5d29 0,0,0), [1,0,0])\n+00005b90: 2025 2063 6f70 7920 696e 206e 6577 2070 % copy in new p\n+00005ba0: 6f73 6974 696f 6e0a 2020 2020 2020 2020 osition. \n+00005bb0: 2020 2020 2020 7468 656e 2074 7261 6e73 then trans\n+00005bc0: 6c61 7465 285b 322c 302c 305d 2920 7d20 late([2,0,0]) } \n+00005bd0: 7b70 6965 7263 6564 5f74 6574 7261 6865 {pierced_tetrahe\n+00005be0: 6472 6f6e 7d0a 416e 6420 7468 6520 7265 dron}.And the re\n+00005bf0: 7375 6c74 2e2e 2e0a 0a00 085b 696d 6167 sult.......[imag\n+00005c00: 6520 7372 633d 2265 7830 3630 2e70 6e67 e src=\"ex060.png\n+00005c10: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n+00005c20: 3036 3020 6f6d 6974 7465 6420 696e 2074 060 omitted in t\n+00005c30: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n+00005c40: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n+00005c50: 5d0a 0a1f 0a46 696c 653a 2073 6b65 7463 ]....File: sketc\n+00005c60: 682e 696e 666f 2c20 204e 6f64 653a 2053 h.info, Node: S\n+00005c70: 7765 7074 206f 626a 6563 7473 2c20 2050 wept objects, P\n+00005c80: 7265 763a 2052 6570 6561 7465 6420 6f62 rev: Repeated ob\n+00005c90: 6a65 6374 732c 2020 5570 3a20 496e 7472 jects, Up: Intr\n+00005ca0: 6f64 7563 7469 6f6e 2062 7920 6578 616d oduction by exam\n+00005cb0: 706c 650a 0a32 2e37 2053 7765 7074 206f ple..2.7 Swept o\n+00005cc0: 626a 6563 7473 0a3d 3d3d 3d3d 3d3d 3d3d bjects.=========\n+00005cd0: 3d3d 3d3d 3d3d 3d3d 0a0a 4d61 6e79 2066 ========..Many f\n+00005ce0: 616d 696c 6961 7220 7368 6170 6573 2063 amiliar shapes c\n+00005cf0: 616e 2062 6520 6765 6e65 7261 7465 6420 an be generated \n+00005d00: 6279 2073 7765 6570 696e 6720 7369 6d70 by sweeping simp\n+00005d10: 6c65 7220 6f6e 6573 2074 6872 6f75 6768 ler ones through\n+00005d20: 0a73 7061 6365 2061 6e64 2063 6f6e 7369 .space and consi\n+00005d30: 6465 7269 6e67 2074 6865 2072 6573 756c dering the resul\n+00005d40: 7469 6e67 2070 6174 682c 2073 7572 6661 ting path, surfa\n+00005d50: 6365 2c20 6f72 2076 6f6c 756d 652e 2020 ce, or volume. \n+00005d60: e280 9853 6b65 7463 68e2 8099 0a69 6d70 ...Sketch....imp\n+00005d70: 6c65 6d65 6e74 7320 7468 6973 2069 6465 lements this ide\n+00005d80: 6120 696e 2074 6865 2073 7765 6570 2063 a in the sweep c\n+00005d90: 6f6d 6d61 6e64 2e0a 2020 6465 6620 6e5f ommand.. def n_\n+00005da0: 7365 6773 2038 0a20 2073 7765 6570 207b segs 8. sweep {\n+00005db0: 206e 5f73 6567 732c 2072 6f74 6174 6528 n_segs, rotate(\n+00005dc0: 3138 3020 2f20 6e5f 7365 6773 2c20 2830 180 / n_segs, (0\n+00005dd0: 2c30 2c30 292c 205b 302c 302c 315d 2920 ,0,0), [0,0,1]) \n+00005de0: 7d20 2831 2c30 2c30 290a 5468 6973 2063 } (1,0,0).This c\n+00005df0: 6f64 6520 7377 6565 7073 2074 6865 2070 ode sweeps the p\n+00005e00: 6f69 6e74 2028 312c 302c 3029 2065 6967 oint (1,0,0) eig\n+00005e10: 6874 2074 696d 6573 2062 7920 726f 7461 ht times by rota\n+00005e20: 7469 6e67 2069 7420 3138 302f 3820 3d0a ting it 180/8 =.\n+00005e30: 3232 2e35 2064 6567 7265 6573 2065 6163 22.5 degrees eac\n+00005e40: 6820 7469 6d65 2061 6e64 2063 6f6e 6e65 h time and conne\n+00005e50: 6374 696e 6720 7468 6520 7265 7375 6c74 cting the result\n+00005e60: 696e 6720 706f 696e 7473 2077 6974 6820 ing points with \n+00005e70: 6c69 6e65 0a73 6567 6d65 6e74 732e 2020 line.segments. \n+00005e80: 5468 6520 6465 6620 7573 6564 2068 6572 The def used her\n+00005e90: 6520 6973 2061 20e2 809c 7363 616c 6172 e is a ...scalar\n+00005ea0: e280 9d20 6465 6669 6e69 7469 6f6e 2e20 ... definition. \n+00005eb0: 2052 6566 6572 656e 6365 7320 746f 0a73 References to.s\n+00005ec0: 6361 6c61 7273 2068 6176 6520 6e6f 2065 calars have no e\n+00005ed0: 6e63 6c6f 7369 6e67 2062 7261 636b 6574 nclosing bracket\n+00005ee0: 7320 6174 2061 6c6c 2e0a 0a2a 204d 656e s at all...* Men\n+00005ef0: 753a 0a0a 2a20 506f 696e 7420 7377 6565 u:..* Point swee\n+00005f00: 7073 3a3a 2020 2020 2020 2020 2020 2020 ps:: \n+00005f10: 2020 2020 5377 6570 7420 706f 696e 7473 Swept points\n+00005f20: 206d 616b 6520 6c69 6e65 7320 616e 6420 make lines and \n+00005f30: 706f 6c79 676f 6e73 2e0a 2a20 506f 6c79 polygons..* Poly\n+00005f40: 6c69 6e65 2073 7765 6570 733a 3a20 2020 line sweeps:: \n+00005f50: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n+00005f60: 6c69 6e65 7320 6d61 6b65 2073 7572 6661 lines make surfa\n+00005f70: 6365 732e 0a2a 204e 6573 7465 6420 7377 ces..* Nested sw\n+00005f80: 6565 7073 3a3a 2020 2020 2020 2020 2020 eeps:: \n+00005f90: 2020 2020 2053 7765 7074 2073 7765 6570 Swept sweep\n+00005fa0: 7320 6172 6520 7573 6566 756c 210a 2a20 s are useful!.* \n+00005fb0: 506f 6c79 676f 6e20 7377 6565 7073 3a3a Polygon sweeps::\n+00005fc0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+00005fd0: 6570 7420 706f 6c79 676f 6e73 206d 616b ept polygons mak\n+00005fe0: 6520 736f 6c69 6473 2e2e 2e0a 2a20 506f e solids....* Po\n+00005ff0: 6c79 6c69 6e65 2073 7765 6570 7320 7769 lyline sweeps wi\n+00006000: 7468 2063 6c6f 7375 7265 3a3a 2020 616e th closure:: an\n+00006010: 6420 736f 2064 6f20 636c 6f73 6564 2070 d so do closed p\n+00006020: 6f6c 796c 696e 6520 7377 6565 7073 2e0a olyline sweeps..\n+00006030: 2a20 4166 6669 6e65 2061 7269 7468 6d65 * Affine arithme\n+00006040: 7469 633a 3a20 2020 2020 2020 2020 2020 tic:: \n+00006050: 536b 6574 6368 2075 7365 6675 6c20 6d61 Sketch useful ma\n+00006060: 7468 2065 7870 7265 7373 696f 6e2e 0a2a th expression..*\n+00006070: 204d 6f72 6520 746f 206c 6561 726e 3a3a More to learn::\n+00006080: 2020 2020 2020 2020 2020 2020 2020 2043 C\n+00006090: 6865 636b 206f 7574 2074 6865 204d 6f62 heck out the Mob\n+000060a0: 6975 7320 7374 7269 7021 0a0a 1f0a 4669 ius strip!....Fi\n+000060b0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n+000060c0: 2020 4e6f 6465 3a20 506f 696e 7420 7377 Node: Point sw\n+000060d0: 6565 7073 2c20 204e 6578 743a 2050 6f6c eeps, Next: Pol\n+000060e0: 796c 696e 6520 7377 6565 7073 2c20 2050 yline sweeps, P\n+000060f0: 7265 763a 2053 7765 7074 206f 626a 6563 rev: Swept objec\n+00006100: 7473 2c20 2055 703a 2053 7765 7074 206f ts, Up: Swept o\n+00006110: 626a 6563 7473 0a0a 322e 372e 3120 506f bjects..2.7.1 Po\n+00006120: 696e 7420 7377 6565 7073 0a2d 2d2d 2d2d int sweeps.-----\n+00006130: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a53 -------------..S\n+00006140: 7765 6570 696e 6720 6120 706f 696e 7420 weeping a point \n+00006150: 6d61 6b65 7320 6120 6f6e 652d 6469 6d65 makes a one-dime\n+00006160: 6e73 696f 6e61 6c20 7061 7468 2c20 7768 nsional path, wh\n+00006170: 6963 6820 6973 2061 2070 6f6c 796c 696e ich is a polylin\n+00006180: 652e 0a53 696e 6365 2077 6520 6861 7665 e..Since we have\n+00006190: 2073 7765 7074 2077 6974 6820 6120 726f swept with a ro\n+000061a0: 7461 7469 6f6e 2c20 7468 6520 7265 7375 tation, the resu\n+000061b0: 6c74 2069 7320 6120 6369 7263 756c 6172 lt is a circular\n+000061c0: 2061 7263 2e20 2048 6572 650a 6973 2077 arc. Here.is w\n+000061d0: 6861 7420 6974 206c 6f6f 6b73 206c 696b hat it looks lik\n+000061e0: 652e 0a0a 0008 5b69 6d61 6765 2073 7263 e.....[image src\n+000061f0: 3d22 6578 3037 302e 706e 6722 2074 6578 =\"ex070.png\" tex\n+00006200: 743d 2249 6d61 6765 2065 7830 3730 206f t=\"Image ex070 o\n+00006210: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n+00006220: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n+00006230: 6f63 756d 656e 742e 2200 085d 0a0a 2020 ocument.\"..].. \n+00006240: 2054 6869 7320 6973 2074 6865 2066 6972 This is the fir\n+00006250: 7374 2065 7861 6d70 6c65 2077 6520 6861 st example we ha\n+00006260: 7665 2073 6565 6e20 6f66 20e2 8098 736b ve seen of ...sk\n+00006270: 6574 6368 e280 9920 6172 6974 686d 6574 etch... arithmet\n+00006280: 6963 2e20 2054 6865 0a65 7870 7265 7373 ic. The.express\n+00006290: 696f 6e20 3138 3020 2f20 6e5f 7365 6773 ion 180 / n_segs\n+000062a0: 2063 6175 7365 7320 7468 6520 6569 6768 causes the eigh\n+000062b0: 7420 726f 7461 7469 6f6e 7320 746f 2061 t rotations to a\n+000062c0: 6464 2074 6f20 3138 302e 2020 4966 0a79 dd to 180. If.y\n+000062d0: 6f75 2772 6520 7061 7969 6e67 2061 7474 ou're paying att\n+000062e0: 656e 7469 6f6e 2c20 796f 7527 6c6c 2068 ention, you'll h\n+000062f0: 6176 6520 616c 7265 6164 7920 6e6f 7465 ave already note\n+00006300: 6420 7468 6174 2074 6865 7265 2061 7265 d that there are\n+00006310: 205f 6e69 6e65 5f0a 706f 696e 7473 2c20 _nine_.points, \n+00006320: 7072 6f64 7563 696e 6720 6569 6768 7420 producing eight \n+00006330: 6c69 6e65 2073 6567 6d65 6e74 732e 0a0a line segments...\n+00006340: 2020 2059 6f75 2063 616e 2063 6175 7365 You can cause\n+00006350: 2074 6865 2073 7765 7074 2070 6f69 6e74 the swept point\n+00006360: 2074 6f20 6765 6e65 7261 7465 2061 2073 to generate a s\n+00006370: 696e 676c 6520 706f 6c79 676f 6e20 7261 ingle polygon ra\n+00006380: 7468 6572 0a74 6861 6e20 6120 706f 6c79 ther.than a poly\n+00006390: 6c69 6e65 2062 7920 7573 696e 6720 7468 line by using th\n+000063a0: 6520 e280 9c63 6c6f 7375 7265 2074 6167 e ...closure tag\n+000063b0: e280 9d20 3c3e 2061 6674 6572 2074 6865 ... <> after the\n+000063c0: 206e 756d 6265 7220 6f66 2073 7765 7074 number of swept\n+000063d0: 0a6f 626a 6563 7473 2e20 2043 6f64 6520 .objects. Code \n+000063e0: 616e 6420 7265 7375 6c74 2066 6f6c 6c6f and result follo\n+000063f0: 770a 2020 6465 6620 6e5f 7365 6773 2038 w. def n_segs 8\n+00006400: 0a20 2073 7765 6570 207b 206e 5f73 6567 . sweep { n_seg\n+00006410: 733c 3e2c 2072 6f74 6174 6528 3138 3020 s<>, rotate(180 \n+00006420: 2f20 6e5f 7365 6773 2c20 2830 2c30 2c30 / n_segs, (0,0,0\n+00006430: 292c 205b 302c 302c 315d 2920 7d20 2831 ), [0,0,1]) } (1\n+00006440: 2c30 2c30 290a 0008 5b69 6d61 6765 2073 ,0,0)...[image s\n+00006450: 7263 3d22 6578 3038 302e 706e 6722 2074 rc=\"ex080.png\" t\n+00006460: 6578 743d 2249 6d61 6765 2065 7830 3830 ext=\"Image ex080\n+00006470: 206f 6d69 7474 6564 2069 6e20 7465 7874 omitted in text\n+00006480: 2076 6572 7369 6f6e 206f 6620 7468 6973 version of this\n+00006490: 2064 6f63 756d 656e 742e 2200 085d 0a0a document.\"..]..\n+000064a0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+000064b0: 6e66 6f2c 2020 4e6f 6465 3a20 506f 6c79 nfo, Node: Poly\n+000064c0: 6c69 6e65 2073 7765 6570 732c 2020 4e65 line sweeps, Ne\n+000064d0: 7874 3a20 4e65 7374 6564 2073 7765 6570 xt: Nested sweep\n+000064e0: 732c 2020 5072 6576 3a20 506f 696e 7420 s, Prev: Point \n+000064f0: 7377 6565 7073 2c20 2055 703a 2053 7765 sweeps, Up: Swe\n+00006500: 7074 206f 626a 6563 7473 0a0a 322e 372e pt objects..2.7.\n+00006510: 3220 506f 6c79 6c69 6e65 2073 7765 6570 2 Polyline sweep\n+00006520: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d s.--------------\n+00006530: 2d2d 2d2d 2d2d 2d0a 0a53 7765 6570 696e -------..Sweepin\n+00006540: 6720 6120 706f 6c79 6c69 6e65 2070 726f g a polyline pro\n+00006550: 6475 6365 7320 6120 7375 7266 6163 6520 duces a surface \n+00006560: 636f 6d70 6f73 6564 206f 6620 6d61 6e79 composed of many\n+00006570: 2066 6163 6573 2e20 2054 6865 0a75 6e62 faces. The.unb\n+00006580: 726f 6b65 6e20 6865 6c69 7820 696e 2074 roken helix in t\n+00006590: 6865 2065 7861 6d70 6c65 202a 6e6f 7465 he example *note\n+000065a0: 2048 656c 6978 2077 6974 6820 6375 6c6c Helix with cull\n+000065b0: 2073 6574 2066 616c 7365 2074 6865 6e0a set false then.\n+000065c0: 7472 7565 3a3a 2069 7320 7072 6f64 7563 true:: is produc\n+000065d0: 6564 2062 7920 7468 6973 2063 6f64 6520 ed by this code \n+000065e0: 2870 6c75 7320 6120 7375 7272 6f75 6e64 (plus a surround\n+000065f0: 696e 6720 7075 7420 726f 7461 7469 6f6e ing put rotation\n+00006600: 2074 6f20 6d61 6b65 0a61 6e20 696e 7465 to make.an inte\n+00006610: 7265 7374 696e 6720 7669 6577 3b20 7468 resting view; th\n+00006620: 6973 2068 6173 2062 6565 6e20 6f6d 6974 is has been omit\n+00006630: 7465 6429 2e0a 2020 6465 6620 4b20 5b30 ted).. def K [0\n+00006640: 2c30 2c31 5d0a 2020 7377 6565 705b 6375 ,0,1]. sweep[cu\n+00006650: 6c6c 3d66 616c 7365 5d20 7b0a 2020 2020 ll=false] {. \n+00006660: 3630 2c20 0a20 2020 2072 6f74 6174 6528 60, . rotate(\n+00006670: 3130 2c20 2830 2c30 2c30 292c 205b 4b5d 10, (0,0,0), [K]\n+00006680: 2920 7468 656e 2074 7261 6e73 6c61 7465 ) then translate\n+00006690: 2831 2f36 202a 205b 4b5d 2920 0a20 207d (1/6 * [K]) . }\n+000066a0: 206c 696e 655b 6c69 6e65 7769 6474 683d line[linewidth=\n+000066b0: 3270 745d 282d 312c 3029 2831 2c30 290a 2pt](-1,0)(1,0).\n+000066c0: 4167 6169 6e2c 2036 3020 7365 676d 656e Again, 60 segmen\n+000066d0: 7473 206f 6620 7468 6520 6865 6c69 7820 ts of the helix \n+000066e0: 6172 6520 7072 6f64 7563 6564 2062 7920 are produced by \n+000066f0: 636f 6e6e 6563 7469 6e67 2036 3120 696e connecting 61 in\n+00006700: 7374 616e 6365 730a 6f66 2074 6865 2073 stances.of the s\n+00006710: 7765 7074 206c 696e 652e 2020 4f70 7469 wept line. Opti\n+00006720: 6f6e 7320 6170 706c 6965 6420 746f 2074 ons applied to t\n+00006730: 6865 2073 7765 6570 2c20 6865 7265 2063 he sweep, here c\n+00006740: 756c 6c3d 6661 6c73 652c 2061 7265 0a74 ull=false, are.t\n+00006750: 7265 6174 6564 2061 7320 6f70 7469 6f6e reated as option\n+00006760: 7320 666f 7220 7468 6520 6765 6e65 7261 s for the genera\n+00006770: 7465 6420 706f 6c79 676f 6e20 6f72 2070 ted polygon or p\n+00006780: 6f6c 796c 696e 652e 2020 4f70 7469 6f6e olyline. Option\n+00006790: 7320 6f66 0a74 6865 2073 7765 7074 206c s of.the swept l\n+000067a0: 696e 6520 6974 7365 6c66 2c20 6865 7265 ine itself, here\n+000067b0: 206c 696e 6577 6964 7468 3d32 7074 2c20 linewidth=2pt, \n+000067c0: 6172 6520 6967 6e6f 7265 642c 2074 686f are ignored, tho\n+000067d0: 7567 6820 7769 7468 2061 0a77 6172 6e69 ugh with a.warni\n+000067e0: 6e67 2e20 2054 6869 7320 6465 6620 6973 ng. This def is\n+000067f0: 2061 20e2 809c 7665 6374 6f72 e280 9d20 a ...vector... \n+00006800: 6465 6669 6e69 7469 6f6e 2c20 7768 6963 definition, whic\n+00006810: 6820 6d75 7374 2062 6520 7265 6665 7265 h must be refere\n+00006820: 6e63 6564 0a77 6974 6820 7371 7561 7265 nced.with square\n+00006830: 2062 7261 636b 6574 732c 2065 2e67 2e20 brackets, e.g. \n+00006840: 5b66 6f6f 5d2e 0a0a 1f0a 4669 6c65 3a20 [foo].....File: \n+00006850: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+00006860: 6465 3a20 4e65 7374 6564 2073 7765 6570 de: Nested sweep\n+00006870: 732c 2020 4e65 7874 3a20 506f 6c79 676f s, Next: Polygo\n+00006880: 6e20 7377 6565 7073 2c20 2050 7265 763a n sweeps, Prev:\n+00006890: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+000068a0: 2c20 2055 703a 2053 7765 7074 206f 626a , Up: Swept obj\n+000068b0: 6563 7473 0a0a 322e 372e 3320 4e65 7374 ects..2.7.3 Nest\n+000068c0: 6564 2073 7765 6570 730a 2d2d 2d2d 2d2d ed sweeps.------\n+000068d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a57 -------------..W\n+000068e0: 6865 6e20 7468 6520 6365 6e74 6572 2070 hen the center p\n+000068f0: 6f69 6e74 206f 6620 726f 7461 7469 6f6e oint of rotation\n+00006900: 2069 7320 6f6d 6974 7465 642c 2074 6865 is omitted, the\n+00006910: 206f 7269 6769 6e20 6973 2061 7373 756d origin is assum\n+00006920: 6564 2e0a 5768 656e 2061 2070 6f69 6e74 ed..When a point\n+00006930: 2068 6173 206f 6e6c 7920 7477 6f20 636f has only two co\n+00006940: 6f72 6469 6e61 7465 732c 2074 6865 7920 ordinates, they \n+00006950: 6172 6520 7461 6b65 6e20 6173 2078 2061 are taken as x a\n+00006960: 6e64 2079 2c20 7769 7468 0a7a 3d30 2061 nd y, with.z=0 a\n+00006970: 7373 756d 6564 2e20 2041 2074 6f72 6f69 ssumed. A toroi\n+00006980: 6420 6973 2074 6865 7265 666f 7265 206f d is therefore o\n+00006990: 6274 6169 6e65 6420 7769 7468 2074 6869 btained with thi\n+000069a0: 7320 636f 6465 2e0a 2020 6465 6620 6e5f s code.. def n_\n+000069b0: 746f 726f 6964 5f73 6567 7320 3230 2020 toroid_segs 20 \n+000069c0: 2064 6566 206e 5f63 6972 636c 655f 7365 def n_circle_se\n+000069d0: 6773 2031 360a 2020 6465 6620 725f 6d69 gs 16. def r_mi\n+000069e0: 6e6f 7220 3120 2020 2020 2020 2020 2064 nor 1 d\n+000069f0: 6566 2072 5f6d 616a 6f72 2031 2e35 0a20 ef r_major 1.5. \n+00006a00: 2073 7765 6570 207b 206e 5f74 6f72 6f69 sweep { n_toroi\n+00006a10: 645f 7365 6773 2c20 726f 7461 7465 2833 d_segs, rotate(3\n+00006a20: 3630 202f 206e 5f74 6f72 6f69 645f 7365 60 / n_toroid_se\n+00006a30: 6773 2c20 5b30 2c31 2c30 5d29 207d 0a20 gs, [0,1,0]) }. \n+00006a40: 2020 2073 7765 6570 207b 206e 5f63 6972 sweep { n_cir\n+00006a50: 636c 655f 7365 6773 2c20 726f 7461 7465 cle_segs, rotate\n+00006a60: 2833 3630 202f 206e 5f63 6972 636c 655f (360 / n_circle_\n+00006a70: 7365 6773 2c20 2872 5f6d 616a 6f72 2c30 segs, (r_major,0\n+00006a80: 2c30 2929 207d 200a 2020 2020 2020 2872 ,0)) } . (r\n+00006a90: 5f6d 616a 6f72 202b 2072 5f6d 696e 6f72 _major + r_minor\n+00006aa0: 2c20 3029 0a20 2020 466f 7220 696e 7475 , 0). For intu\n+00006ab0: 6974 696f 6e2c 2074 6865 2069 6465 6120 ition, the idea \n+00006ac0: 6f66 2074 6865 2063 6f64 6520 6973 2074 of the code is t\n+00006ad0: 6f20 736b 6574 6368 2061 2063 6972 636c o sketch a circl\n+00006ae0: 6520 746f 2074 6865 0a72 6967 6874 206f e to the.right o\n+00006af0: 6620 7468 6520 6f72 6967 696e 2069 6e20 f the origin in \n+00006b00: 7468 6520 7879 2d70 6c61 6e65 2c20 7468 the xy-plane, th\n+00006b10: 656e 2072 6f74 6174 6520 7468 6174 2063 en rotate that c\n+00006b20: 6972 636c 6520 226f 7574 206f 6620 7468 ircle \"out of th\n+00006b30: 650a 706c 616e 6522 2061 626f 7574 2074 e.plane\" about t\n+00006b40: 6865 2079 2d61 7869 7320 746f 206d 616b he y-axis to mak\n+00006b50: 6520 7468 6520 6669 6e61 6c20 6669 6775 e the final figu\n+00006b60: 7265 2e20 2054 6869 7320 7072 6f64 7563 re. This produc\n+00006b70: 6573 2074 6865 0a66 6f6c 6c6f 7769 6e67 es the.following\n+00006b80: 2e20 2028 4120 7669 6577 2072 6f74 6174 . (A view rotat\n+00006b90: 696f 6e20 616e 6420 736f 6d65 2061 7865 ion and some axe\n+00006ba0: 7320 6861 7665 2062 6565 6e20 6164 6465 s have been adde\n+00006bb0: 642e 290a 0a00 085b 696d 6167 6520 7372 d.)....[image sr\n+00006bc0: 633d 2265 7830 3930 2e70 6e67 2220 7465 c=\"ex090.png\" te\n+00006bd0: 7874 3d22 496d 6167 6520 6578 3039 3020 xt=\"Image ex090 \n+00006be0: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n+00006bf0: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n+00006c00: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a20 document.\"..].. \n+00006c10: 2020 5468 6973 2065 7861 6d70 6c65 2061 This example a\n+00006c20: 6c73 6f20 7368 6f77 7320 7468 6174 2074 lso shows that t\n+00006c30: 6865 2073 7765 7074 206f 626a 6563 7420 he swept object \n+00006c40: 6d61 7920 6974 7365 6c66 2062 6520 616e may itself be an\n+00006c50: 6f74 6865 720a e280 9873 7765 6570 e280 other....sweep..\n+00006c60: 992e 2020 496e 2066 6163 742c 2069 7420 .. In fact, it \n+00006c70: 6d61 7920 6265 205f 616e 795f 20e2 8098 may be _any_ ...\n+00006c80: 736b 6574 6368 e280 9920 6578 7072 6573 sketch... expres\n+00006c90: 7369 6f6e 2074 6861 7420 7265 7375 6c74 sion that result\n+00006ca0: 7320 696e 2061 0a6c 6973 7420 6f66 206f s in a.list of o\n+00006cb0: 6e65 206f 7220 6d6f 7265 2070 6f69 6e74 ne or more point\n+00006cc0: 7320 6f72 2c20 616c 7465 726e 6174 656c s or, alternatel\n+00006cd0: 792c 2061 206c 6973 7420 6f66 206f 6e65 y, a list of one\n+00006ce0: 206f 7220 6d6f 7265 0a70 6f6c 796c 696e or more.polylin\n+00006cf0: 6573 2061 6e64 2070 6f6c 7967 6f6e 732e es and polygons.\n+00006d00: 2020 5468 6520 6c61 7474 6572 206b 696e The latter kin\n+00006d10: 6420 6f66 206c 6973 7420 6361 6e20 6265 d of list can be\n+00006d20: 2063 7265 6174 6564 2077 6974 6820 610a created with a.\n+00006d30: 7b20 7d2d 656e 636c 6f73 6564 2062 6c6f { }-enclosed blo\n+00006d40: 636b 2c20 7065 7268 6170 7320 666f 6c6c ck, perhaps foll\n+00006d50: 6f77 696e 6720 6120 7075 7420 6f72 2072 owing a put or r\n+00006d60: 6570 6561 742e 0a0a 1f0a 4669 6c65 3a20 epeat.....File: \n+00006d70: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+00006d80: 6465 3a20 506f 6c79 676f 6e20 7377 6565 de: Polygon swee\n+00006d90: 7073 2c20 204e 6578 743a 2050 6f6c 796c ps, Next: Polyl\n+00006da0: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n+00006db0: 636c 6f73 7572 652c 2020 5072 6576 3a20 closure, Prev: \n+00006dc0: 4e65 7374 6564 2073 7765 6570 732c 2020 Nested sweeps, \n+00006dd0: 5570 3a20 5377 6570 7420 6f62 6a65 6374 Up: Swept object\n+00006de0: 730a 0a32 2e37 2e34 2050 6f6c 7967 6f6e s..2.7.4 Polygon\n+00006df0: 2073 7765 6570 730a 2d2d 2d2d 2d2d 2d2d sweeps.--------\n+00006e00: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 5377 ------------..Sw\n+00006e10: 6565 7069 6e67 2061 2070 6f6c 7967 6f6e eeping a polygon\n+00006e20: 2063 7265 6174 6573 2061 2063 6c6f 7365 creates a close\n+00006e30: 6420 7375 7266 6163 6520 7769 7468 2070 d surface with p\n+00006e40: 6f6c 7967 6f6e 7320 6174 2074 6865 2065 olygons at the e\n+00006e50: 6e64 732c 0a77 6869 6368 2061 7265 206a nds,.which are j\n+00006e60: 7573 7420 636f 7069 6573 206f 6620 7468 ust copies of th\n+00006e70: 6520 6f72 6967 696e 616c 2c20 6170 7072 e original, appr\n+00006e80: 6f70 7269 6174 656c 7920 706f 7369 7469 opriately positi\n+00006e90: 6f6e 6564 2e20 202a 4e6f 7465 0a53 6f6c oned. *Note.Sol\n+00006ea0: 6964 2063 6f69 6c20 6578 616d 706c 653a id coil example:\n+00006eb0: 3a2e 2020 4f70 7469 6f6e 7320 6f6e 2074 :. Options on t\n+00006ec0: 6865 2073 7765 7074 2070 6f6c 7967 6f6e he swept polygon\n+00006ed0: 2c20 6966 2074 6865 7920 6578 6973 742c , if they exist,\n+00006ee0: 2061 7265 0a61 7070 6c69 6564 2074 6f20 are.applied to \n+00006ef0: 7468 6520 656e 6473 2e20 204f 7468 6572 the ends. Other\n+00006f00: 7769 7365 2074 6865 2073 7765 6570 206f wise the sweep o\n+00006f10: 7074 696f 6e73 2061 7265 2075 7365 6420 ptions are used \n+00006f20: 7468 726f 7567 686f 7574 2e0a 0a1f 0a46 throughout.....F\n+00006f30: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+00006f40: 2c20 204e 6f64 653a 2050 6f6c 796c 696e , Node: Polylin\n+00006f50: 6520 7377 6565 7073 2077 6974 6820 636c e sweeps with cl\n+00006f60: 6f73 7572 652c 2020 4e65 7874 3a20 4166 osure, Next: Af\n+00006f70: 6669 6e65 2061 7269 7468 6d65 7469 632c fine arithmetic,\n+00006f80: 2020 5072 6576 3a20 506f 6c79 676f 6e20 Prev: Polygon \n+00006f90: 7377 6565 7073 2c20 2055 703a 2053 7765 sweeps, Up: Swe\n+00006fa0: 7074 206f 626a 6563 7473 0a0a 322e 372e pt objects..2.7.\n+00006fb0: 3520 506f 6c79 6c69 6e65 2073 7765 6570 5 Polyline sweep\n+00006fc0: 7320 7769 7468 2063 6c6f 7375 7265 0a2d s with closure.-\n+00006fd0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00006fe0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00006ff0: 2d2d 2d0a 0a41 2070 6f6c 796c 696e 6520 ---..A polyline \n-00007000: 7377 6565 7020 7769 7468 2061 2063 6c6f sweep with a clo\n-00007010: 7375 7265 2074 6167 2063 7265 6174 6573 sure tag creates\n-00007020: 2061 6e6f 7468 6572 206b 696e 6420 6f66 another kind of\n-00007030: 2063 6c6f 7365 640a 7375 7266 6163 652e closed.surface.\n-00007040: 2020 4669 7273 742c 2074 6865 2070 6f6c First, the pol\n-00007050: 796c 696e 6520 7365 676d 656e 7473 2061 yline segments a\n-00007060: 7265 2063 6f6e 6e65 6374 6564 2062 7920 re connected by \n-00007070: 6661 6365 732c 206a 7573 7420 6173 0a77 faces, just as.w\n-00007080: 6974 686f 7574 2074 6865 2063 6c6f 7375 ithout the closu\n-00007090: 7265 2074 6167 2e20 2054 6865 6e2c 2065 re tag. Then, e\n-000070a0: 6163 6820 7365 7420 6f66 2065 6e64 2070 ach set of end p\n-000070b0: 6f69 6e74 7320 6973 206a 6f69 6e65 6420 oints is joined \n-000070c0: 746f 206d 616b 650a 6120 706f 6c79 676f to make.a polygo\n-000070d0: 6e2c 206f 6e65 2066 6f72 2065 6163 6820 n, one for each \n-000070e0: 656e 642e 2020 4120 636f 6465 2066 6f72 end. A code for\n-000070f0: 2073 6576 6572 616c 2076 6965 7773 206f several views o\n-00007100: 6620 6120 6379 6c69 6e64 7269 6361 6c0a f a cylindrical.\n-00007110: 7072 6973 6d20 666f 6c6c 6f77 732e 0a20 prism follows.. \n-00007120: 2064 6566 206e 5f63 796c 5f73 6567 7320 def n_cyl_segs \n-00007130: 3230 2020 6465 6620 6e5f 7669 6577 7320 20 def n_views \n-00007140: 3520 2064 6566 2049 205b 312c 302c 305d 5 def I [1,0,0]\n-00007150: 0a20 2064 6566 2065 6e64 6f70 7473 205b . def endopts [\n-00007160: 6669 6c6c 636f 6c6f 723d 6c69 6768 7467 fillcolor=lightg\n-00007170: 7261 795d 0a20 2072 6570 6561 7420 7b20 ray]. repeat { \n-00007180: 6e5f 7669 6577 732c 2072 6f74 6174 6528 n_views, rotate(\n-00007190: 3138 302f 6e5f 7669 6577 732c 205b 495d 180/n_views, [I]\n-000071a0: 2920 7468 656e 2074 7261 6e73 6c61 7465 ) then translate\n-000071b0: 285b 495d 202a 2032 2e31 2920 7d20 0a20 ([I] * 2.1) } . \n-000071c0: 2020 2073 7765 6570 5b65 6e64 6f70 7473 sweep[endopts\n-000071d0: 5d7b 206e 5f63 796c 5f73 6567 733c 3e2c ]{ n_cyl_segs<>,\n-000071e0: 2072 6f74 6174 6528 3336 302f 6e5f 6379 rotate(360/n_cy\n-000071f0: 6c5f 7365 6773 2c20 5b30 2c31 2c30 5d29 l_segs, [0,1,0])\n-00007200: 207d 200a 2020 2020 2020 6c69 6e65 5b66 } . line[f\n-00007210: 696c 6c63 6f6c 6f72 3d77 6869 7465 5d28 illcolor=white](\n-00007220: 312c 2d31 2928 312c 3129 0a49 7420 7072 1,-1)(1,1).It pr\n-00007230: 6f64 7563 6573 2074 6869 7320 6472 6177 oduces this draw\n-00007240: 696e 672e 0a0a 0008 5b69 6d61 6765 2073 ing.....[image s\n-00007250: 7263 3d22 6578 3131 302e 706e 6722 2074 rc=\"ex110.png\" t\n-00007260: 6578 743d 2249 6d61 6765 2065 7831 3130 ext=\"Image ex110\n-00007270: 206f 6d69 7474 6564 2069 6e20 7465 7874 omitted in text\n-00007280: 2076 6572 7369 6f6e 206f 6620 7468 6973 version of this\n-00007290: 2064 6f63 756d 656e 742e 2200 085d 0a0a document.\"..]..\n-000072a0: 5468 6520 6f70 7469 6f6e 7320 6f66 2074 The options of t\n-000072b0: 6865 2073 7765 7074 206c 696e 652c 2069 he swept line, i\n-000072c0: 6620 616e 792c 2061 7265 2061 7070 6c69 f any, are appli\n-000072d0: 6564 2074 6f20 7468 6520 6661 6365 7320 ed to the faces \n-000072e0: 7072 6f64 7563 6564 0a62 7920 7377 6565 produced.by swee\n-000072f0: 7069 6e67 2074 6865 206c 696e 652c 2062 ping the line, b\n-00007300: 7574 206e 6f74 2074 6865 2065 6e64 2070 ut not the end p\n-00007310: 6f6c 7967 6f6e 732e 2020 4f74 6865 7277 olygons. Otherw\n-00007320: 6973 652c 2074 6865 2073 7765 6570 0a6f ise, the sweep.o\n-00007330: 7074 696f 6e73 2061 7265 2061 7070 6c69 ptions are appli\n-00007340: 6564 2074 6872 6f75 6768 6f75 742e 2020 ed throughout. \n-00007350: 5468 6520 6465 6620 696e 2074 6869 7320 The def in this \n-00007360: 6578 616d 706c 6520 6973 2061 6e20 e280 example is an ..\n-00007370: 9c6f 7074 696f 6ee2 809d 0a64 6566 696e .option....defin\n-00007380: 6974 696f 6e2e 2020 5265 6665 7265 6e63 ition. Referenc\n-00007390: 6573 2074 6f20 6f70 7469 6f6e 7320 6d75 es to options mu\n-000073a0: 7374 2062 6520 656e 636c 6f73 6564 2069 st be enclosed i\n-000073b0: 6e20 7371 7561 7265 2062 7261 636b 6574 n square bracket\n-000073c0: 732c 0a65 2e67 2e20 2020 5b66 6f6f 5d2e s,.e.g. [foo].\n-000073d0: 2020 596f 7520 6361 6e20 636f 6e63 6174 You can concat\n-000073e0: 656e 6174 6520 7365 7665 7261 6c20 7365 enate several se\n-000073f0: 7473 206f 6620 6f70 7469 6f6e 7320 7769 ts of options wi\n-00007400: 7468 2061 2073 696e 676c 650a 7265 6665 th a single.refe\n-00007410: 7265 6e63 652c 2065 2e67 2e20 2020 5b63 rence, e.g. [c\n-00007420: 6f6c 6f72 2c20 7369 7a65 2c20 7374 796c olor, size, styl\n-00007430: 655d 2020 776f 756c 6420 6361 7573 6520 e] would cause \n-00007440: 7468 6520 6f70 7469 6f6e 0a64 6566 696e the option.defin\n-00007450: 6974 696f 6e73 2066 6f72 20e2 8098 636f itions for ...co\n-00007460: 6c6f 72e2 8099 2c20 e280 9873 697a 65e2 lor..., ...size.\n-00007470: 8099 2c20 616e 6420 e280 9873 7479 6c65 .., and ...style\n-00007480: e280 9920 746f 2061 7070 6561 7220 696e ... to appear in\n-00007490: 2073 6571 7565 6e63 6520 696e 0a74 6865 sequence in.the\n-000074a0: 206f 7574 7075 7420 6372 6561 7465 6420 output created \n-000074b0: 6279 2074 6865 20e2 8098 736b 6574 6368 by the ...sketch\n-000074c0: e280 9920 636f 6d6d 616e 6420 636f 6e74 ... command cont\n-000074d0: 6169 6e69 6e67 2074 6865 2072 6566 6572 aining the refer\n-000074e0: 656e 6365 2e0a 4861 7070 696c 792c 2074 ence..Happily, t\n-000074f0: 6865 2073 796e 7461 7820 6f66 20e2 8098 he syntax of ...\n-00007500: 736b 6574 6368 e280 9920 6973 2073 7563 sketch... is suc\n-00007510: 6820 7468 6174 206f 7074 696f 6e73 2072 h that options r\n-00007520: 6566 6572 656e 6365 7320 6361 6e0a 6e65 eferences can.ne\n-00007530: 7665 7220 6265 2063 6f6e 6675 7365 6420 ver be confused \n-00007540: 7769 7468 2076 6563 746f 7220 7265 6665 with vector refe\n-00007550: 7265 6e63 6573 2e20 2057 6869 6c65 206e rences. While n\n-00007560: 6f74 2061 7070 6172 656e 7420 696e 2074 ot apparent in t\n-00007570: 6869 730a 6578 616d 706c 652c 206f 7074 his.example, opt\n-00007580: 696f 6e73 2072 6566 6572 656e 6365 7320 ions references \n-00007590: 6172 6520 7573 6566 756c 2077 6865 6e20 are useful when \n-000075a0: 6465 6669 6e69 6e67 206d 616e 7920 6f62 defining many ob\n-000075b0: 6a65 6374 7320 7769 7468 2061 0a73 696d jects with a.sim\n-000075c0: 696c 6172 2061 7070 6561 7261 6e63 652e ilar appearance.\n-000075d0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-000075e0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4166 .info, Node: Af\n-000075f0: 6669 6e65 2061 7269 7468 6d65 7469 632c fine arithmetic,\n-00007600: 2020 4e65 7874 3a20 4d6f 7265 2074 6f20 Next: More to \n-00007610: 6c65 6172 6e2c 2020 5072 6576 3a20 506f learn, Prev: Po\n-00007620: 6c79 6c69 6e65 2073 7765 6570 7320 7769 lyline sweeps wi\n-00007630: 7468 2063 6c6f 7375 7265 2c20 2055 703a th closure, Up:\n-00007640: 2053 7765 7074 206f 626a 6563 7473 0a0a Swept objects..\n-00007650: 322e 372e 3620 4166 6669 6e65 2061 7269 2.7.6 Affine ari\n-00007660: 7468 6d65 7469 630a 2d2d 2d2d 2d2d 2d2d thmetic.--------\n-00007670: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ---------------.\n-00007680: 0a54 6865 2061 7269 7468 6d65 7469 6320 .The arithmetic \n-00007690: 5b49 5d20 2a20 322e 3120 6162 6f76 6520 [I] * 2.1 above \n-000076a0: 6869 6e74 7320 6174 2061 206c 6172 6765 hints at a large\n-000076b0: 7220 7472 7574 682e 2020 e280 9853 6b65 r truth. ...Ske\n-000076c0: 7463 68e2 8099 0a6f 7065 7261 746f 7273 tch....operators\n-000076d0: 2077 6f72 6b20 6f6e 2073 6361 6c61 7273 work on scalars\n-000076e0: 2c20 7665 6374 6f72 732c 2070 6f69 6e74 , vectors, point\n-000076f0: 732c 2061 6e64 2074 7261 6e73 666f 726d s, and transform\n-00007700: 7320 6163 636f 7264 696e 6720 746f 0a74 s according to.t\n-00007710: 6865 2067 656e 6572 616c 2072 756c 6573 he general rules\n-00007720: 206f 6620 e280 9c61 6666 696e 6520 616c of ...affine al\n-00007730: 6765 6272 61e2 809d 2e20 2054 6869 7320 gebra.... 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The followi\n-00007ca0: 6e67 2077 6f72 6b73 2c20 7468 6f75 6768 ng works, though\n-00007cb0: 2069 7427 7320 610a 6c69 7474 6c65 2063 it's a.little c\n-00007cc0: 756d 6265 7273 6f6d 652e 0a20 206c 696e umbersome.. lin\n-00007cd0: 655b 6172 726f 7773 3d2a 2d3e 5d28 6e31 e[arrows=*->](n1\n-00007ce0: 2928 286e 3129 2778 2b28 4e29 2778 2c20 )((n1)'x+(N)'x, \n-00007cf0: 286e 3129 2779 2b28 4e29 2779 2c20 286e (n1)'y+(N)'y, (n\n-00007d00: 3129 277a 2b28 4e29 277a 290a 4f62 7669 1)'z+(N)'z).Obvi\n-00007d10: 6f75 736c 792c 2074 6865 20e2 809c 7469 ously, the ...ti\n-00007d20: 636b 206f 7065 7261 746f 72e2 809d 20e2 ck operator... .\n-00007d30: 8098 2778 e280 9920 6578 7472 6163 7473 ..'x... extracts\n-00007d40: 2063 6f6d 706f 6e65 6e74 7320 6f66 2070 components of p\n-00007d50: 6f69 6e74 7320 616e 640a 7665 6374 6f72 oints and.vector\n-00007d60: 732e 0a0a 1f0a 4669 6c65 3a20 736b 6574 s.....File: sket\n-00007d70: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-00007d80: 4d6f 7265 2074 6f20 6c65 6172 6e2c 2020 More to learn, \n-00007d90: 5072 6576 3a20 4166 6669 6e65 2061 7269 Prev: Affine ari\n-00007da0: 7468 6d65 7469 632c 2020 5570 3a20 5377 thmetic, Up: Sw\n-00007db0: 6570 7420 6f62 6a65 6374 730a 0a32 2e37 ept objects..2.7\n-00007dc0: 2e37 204d 6f72 6520 746f 206c 6561 726e .7 More to learn\n-00007dd0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n-00007de0: 2d2d 2d2d 0a0a 5468 6973 2069 7320 6e6f ----..This is no\n-00007df0: 7420 7468 6520 656e 6420 6f66 2074 6865 t the end of the\n-00007e00: 2073 746f 7279 206f 6e20 7377 6565 7073 story on sweeps\n-00007e10: 2120 2057 6520 696e 7669 7465 2074 6865 ! We invite the\n-00007e20: 2072 6561 6465 7220 696e 746f 0a74 6865 reader into.the\n-00007e30: 206d 6169 6e20 626f 6479 206f 6620 7468 main body of th\n-00007e40: 6973 2064 6f63 756d 656e 7461 7469 6f6e is documentation\n-00007e50: 202a 6e6f 7465 2053 7765 6570 733a 3a20 *note Sweeps:: \n-00007e60: 746f 206c 6561 726e 206d 6f72 652e 0a0a to learn more...\n-00007e70: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n-00007e80: 3132 302e 706e 6722 2074 6578 743d 2249 120.png\" text=\"I\n-00007e90: 6d61 6765 2065 7831 3230 206f 6d69 7474 mage ex120 omitt\n-00007ea0: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n-00007eb0: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n-00007ec0: 656e 742e 2200 085d 0a0a 5768 6f20 6b6e ent.\"..]..Who kn\n-00007ed0: 6f77 7320 7768 6572 6520 796f 7527 6c6c ows where you'll\n-00007ee0: 2066 696e 6973 683f 0a0a 1f0a 4669 6c65 finish?....File\n-00007ef0: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-00007f00: 4e6f 6465 3a20 496e 7075 7420 6c61 6e67 Node: Input lang\n-00007f10: 7561 6765 2c20 204e 6578 743a 2042 7569 uage, Next: Bui\n-00007f20: 6c64 696e 6720 6120 6472 6177 696e 672c lding a drawing,\n-00007f30: 2020 5072 6576 3a20 496e 7472 6f64 7563 Prev: Introduc\n-00007f40: 7469 6f6e 2062 7920 6578 616d 706c 652c tion by example,\n-00007f50: 2020 5570 3a20 546f 700a 0a33 2049 6e70 Up: Top..3 Inp\n-00007f60: 7574 206c 616e 6775 6167 650a 2a2a 2a2a ut language.****\n-00007f70: 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a 5468 ************..Th\n-00007f80: 6973 2063 6861 7074 6572 2064 6573 6372 is chapter descr\n-00007f90: 6962 6573 2074 6865 20e2 8098 736b 6574 ibes the ...sket\n-00007fa0: 6368 e280 9920 696e 7075 7420 6c61 6e67 ch... input lang\n-00007fb0: 7561 6765 2069 6e20 6465 7461 696c 2e0a uage in detail..\n-00007fc0: 0a2a 204d 656e 753a 0a0a 2a20 4c61 6e67 .* Menu:..* Lang\n-00007fd0: 7561 6765 2062 6173 6963 733a 3a20 2020 uage basics:: \n-00007fe0: 2020 2020 2020 2020 2020 4361 7365 2c20 Case, \n-00007ff0: 7370 6163 652c 2063 6f6d 6d65 6e74 732c space, comments,\n-00008000: 2069 6e63 6c75 6465 2066 696c 6573 2e0a include files..\n-00008010: 2a20 4472 6177 6162 6c65 733a 3a20 2020 * Drawables:: \n-00008020: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00008030: 5468 696e 6773 2074 6861 7420 6361 6e20 Things that can \n-00008040: 6265 2064 7261 776e 2e0a 2a20 4465 6669 be drawn..* Defi\n-00008050: 6e69 7469 6f6e 733a 3a20 2020 2020 2020 nitions:: \n-00008060: 2020 2020 2020 2020 2020 4769 7669 6e67 Giving\n-00008070: 2074 6869 6e67 7320 6e61 6d65 732e 0a2a things names..*\n-00008080: 2047 6c6f 6261 6c20 656e 7669 726f 6e6d Global environm\n-00008090: 656e 743a 3a20 2020 2020 2020 2020 2041 ent:: A\n-000080a0: 6666 6563 7420 7468 6520 656e 7469 7265 ffect the entire\n-000080b0: 2064 7261 7769 6e67 2e0a 0a1f 0a46 696c drawing.....Fil\n-000080c0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-000080d0: 204e 6f64 653a 204c 616e 6775 6167 6520 Node: Language \n-000080e0: 6261 7369 6373 2c20 204e 6578 743a 2044 basics, Next: D\n-000080f0: 7261 7761 626c 6573 2c20 2050 7265 763a rawables, Prev:\n-00008100: 2049 6e70 7574 206c 616e 6775 6167 652c Input language,\n-00008110: 2020 5570 3a20 496e 7075 7420 6c61 6e67 Up: Input lang\n-00008120: 7561 6765 0a0a 332e 3120 4261 7369 6373 uage..3.1 Basics\n-00008130: 0a3d 3d3d 3d3d 3d3d 3d3d 3d0a 0ae2 8098 .==========.....\n-00008140: 536b 6574 6368 e280 9920 696e 7075 7420 Sketch... input \n-00008150: 6973 2070 6c61 696e 2041 5343 4949 2074 is plain ASCII t\n-00008160: 6578 742c 2075 7375 616c 6c79 2073 746f ext, usually sto\n-00008170: 7265 6420 696e 2061 6e20 696e 7075 7420 red in an input \n-00008180: 6669 6c65 2e20 2049 740a 6465 7363 7269 file. 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The rese\n-00008b40: 7276 6564 2077 6f72 6473 2061 7265 20e2 rved words are .\n-00008b50: 8098 6163 6f73 e280 9920 e280 9861 7369 ..acos... ...asi\n-00008b60: 6ee2 8099 20e2 8098 6174 616e 32e2 8099 n... ...atan2...\n-00008b70: 0ae2 8098 636f 73e2 8099 20e2 8098 696e ....cos... ...in\n-00008b80: 7665 7273 65e2 8099 20e2 8098 7065 7273 verse... ...pers\n-00008b90: 7065 6374 6976 65e2 8099 20e2 8098 7072 pective... ...pr\n-00008ba0: 6f6a 6563 74e2 8099 20e2 8098 726f 7461 oject... ...rota\n-00008bb0: 7465 e280 9920 e280 9873 6361 6c65 e280 te... ...scale..\n-00008bc0: 9920 e280 9873 696e e280 9920 e280 9873 . ...sin... ...s\n-00008bd0: 7065 6369 616c e280 990a e280 9873 7172 pecial.......sqr\n-00008be0: 74e2 8099 20e2 8098 7472 616e 736c 6174 t... ...translat\n-00008bf0: 65e2 8099 20e2 8098 756e 6974 e280 9920 e... ...unit... \n-00008c00: 616e 6420 e280 9876 6965 77e2 8099 2e0a and ...view.....\n-00008c10: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00008c20: 696e 666f 2c20 204e 6f64 653a 204c 6974 info, Node: Lit\n-00008c30: 6572 616c 732c 2020 4e65 7874 3a20 4172 erals, Next: Ar\n-00008c40: 6974 686d 6574 6963 2c20 2050 7265 763a ithmetic, Prev:\n-00008c50: 204b 6579 2061 6e64 2072 6573 6572 7665 Key and reserve\n-00008c60: 6420 776f 7264 732c 2020 5570 3a20 4c61 d words, Up: La\n-00008c70: 6e67 7561 6765 2062 6173 6963 730a 0a33 nguage basics..3\n-00008c80: 2e31 2e33 204c 6974 6572 616c 730a 2d2d .1.3 Literals.--\n-00008c90: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 4c69 ------------..Li\n-00008ca0: 7465 7261 6c73 2069 6e20 e280 9873 6b65 terals in ...ske\n-00008cb0: 7463 68e2 8099 2069 6e63 6c75 6465 2073 tch... include s\n-00008cc0: 6361 6c61 7273 2c20 706f 696e 7473 2c20 calars, points, \n-00008cd0: 7665 6374 6f72 732c 2061 6e64 2074 7261 vectors, and tra\n-00008ce0: 6e73 666f 726d 732e 0a4c 6974 6572 616c nsforms..Literal\n-00008cf0: 732c 2061 6c6f 6e67 2077 6974 6820 6465 s, along with de\n-00008d00: 6669 6e65 6420 6f62 6a65 6374 2072 6566 fined object ref\n-00008d10: 6572 656e 6365 732c 2061 7265 2075 7365 erences, are use\n-00008d20: 6420 696e 2061 7269 7468 6d65 7469 630a d in arithmetic.\n-00008d30: 6578 7072 6573 7369 6f6e 732e 2020 2a4e expressions. *N\n-00008d40: 6f74 6520 4172 6974 686d 6574 6963 3a3a ote Arithmetic::\n-00008d50: 2e0a 0a2a 204d 656e 753a 0a0a 2a20 5363 ...* Menu:..* Sc\n-00008d60: 616c 6172 206c 6974 6572 616c 733a 3a20 alar literals:: \n-00008d70: 2020 2020 2020 2020 2020 2020 4a75 7374 Just\n-00008d80: 2074 6865 206e 756d 6265 7273 2e0a 2a20 the numbers..* \n-00008d90: 506f 696e 7420 616e 6420 7665 6374 6f72 Point and vector\n-00008da0: 206c 6974 6572 616c 733a 3a20 2020 3364 literals:: 3d\n-00008db0: 2071 7561 6e74 6974 6965 732e 0a2a 2054 quantities..* T\n-00008dc0: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n-00008dd0: 733a 3a20 2020 2020 2020 2020 204d 6174 s:: Mat\n-00008de0: 7269 7820 666f 726d 2e0a 0a1f 0a46 696c rix form.....Fil\n-00008df0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-00008e00: 204e 6f64 653a 2053 6361 6c61 7220 6c69 Node: Scalar li\n-00008e10: 7465 7261 6c73 2c20 204e 6578 743a 2050 terals, Next: P\n-00008e20: 6f69 6e74 2061 6e64 2076 6563 746f 7220 oint and vector \n-00008e30: 6c69 7465 7261 6c73 2c20 2050 7265 763a literals, Prev:\n-00008e40: 204c 6974 6572 616c 732c 2020 5570 3a20 Literals, Up: \n-00008e50: 4c69 7465 7261 6c73 0a0a 332e 312e 332e Literals..3.1.3.\n-00008e60: 3120 5363 616c 6172 206c 6974 6572 616c 1 Scalar literal\n-00008e70: 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e s...............\n-00008e80: 2e2e 2e2e 2e2e 2e2e 2e0a 0a53 6361 6c61 ...........Scala\n-00008e90: 7220 6c69 7465 7261 6c73 2061 7265 2070 r literals are p\n-00008ea0: 6f73 6974 6976 6520 666c 6f61 7469 6e67 ositive floating\n-00008eb0: 2070 6f69 6e74 206e 756d 6265 7273 2077 point numbers w\n-00008ec0: 6974 6820 7379 6e74 6178 0a61 6363 6f72 ith syntax.accor\n-00008ed0: 6469 6e67 2074 6f20 4320 636f 6e76 656e ding to C conven\n-00008ee0: 7469 6f6e 732e 2020 5468 6520 666f 6c6c tions. The foll\n-00008ef0: 6f77 696e 6720 6172 6520 736f 6d65 2065 owing are some e\n-00008f00: 7861 6d70 6c65 732e 0a20 2020 2020 3020 xamples.. 0 \n-00008f10: 3130 3034 202e 3030 3120 382e 3331 3433 1004 .001 8.3143\n-00008f20: 2033 2e20 312e 3630 452d 3139 2036 2e30 3. 1.60E-19 6.0\n-00008f30: 3265 2b32 330a 5363 616c 6172 206c 6974 2e+23.Scalar lit\n-00008f40: 6572 616c 7320 6d61 7920 6e6f 7420 636f erals may not co\n-00008f50: 6e74 6169 6e20 656d 6265 6464 6564 2073 ntain embedded s\n-00008f60: 7061 6365 732e 0a0a 1f0a 4669 6c65 3a20 paces.....File: \n-00008f70: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-00008f80: 6465 3a20 506f 696e 7420 616e 6420 7665 de: Point and ve\n-00008f90: 6374 6f72 206c 6974 6572 616c 732c 2020 ctor literals, \n-00008fa0: 4e65 7874 3a20 5472 616e 7366 6f72 6d20 Next: Transform \n-00008fb0: 6c69 7465 7261 6c73 2c20 2050 7265 763a literals, Prev:\n-00008fc0: 2053 6361 6c61 7220 6c69 7465 7261 6c73 Scalar literals\n-00008fd0: 2c20 2055 703a 204c 6974 6572 616c 730a , Up: Literals.\n-00008fe0: 0a33 2e31 2e33 2e32 2050 6f69 6e74 2061 .3.1.3.2 Point a\n-00008ff0: 6e64 2076 6563 746f 7220 6c69 7465 7261 nd vector litera\n-00009000: 6c73 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ls..............\n+00006ff0: 2d0a 0a41 2070 6f6c 796c 696e 6520 7377 -..A polyline sw\n+00007000: 6565 7020 7769 7468 2061 2063 6c6f 7375 eep with a closu\n+00007010: 7265 2074 6167 2063 7265 6174 6573 2061 re tag creates a\n+00007020: 6e6f 7468 6572 206b 696e 6420 6f66 2063 nother kind of c\n+00007030: 6c6f 7365 640a 7375 7266 6163 652e 2020 losed.surface. \n+00007040: 4669 7273 742c 2074 6865 2070 6f6c 796c First, the polyl\n+00007050: 696e 6520 7365 676d 656e 7473 2061 7265 ine segments are\n+00007060: 2063 6f6e 6e65 6374 6564 2062 7920 6661 connected by fa\n+00007070: 6365 732c 206a 7573 7420 6173 0a77 6974 ces, just as.wit\n+00007080: 686f 7574 2074 6865 2063 6c6f 7375 7265 hout the closure\n+00007090: 2074 6167 2e20 2054 6865 6e2c 2065 6163 tag. Then, eac\n+000070a0: 6820 7365 7420 6f66 2065 6e64 2070 6f69 h set of end poi\n+000070b0: 6e74 7320 6973 206a 6f69 6e65 6420 746f nts is joined to\n+000070c0: 206d 616b 650a 6120 706f 6c79 676f 6e2c make.a polygon,\n+000070d0: 206f 6e65 2066 6f72 2065 6163 6820 656e one for each en\n+000070e0: 642e 2020 4120 636f 6465 2066 6f72 2073 d. A code for s\n+000070f0: 6576 6572 616c 2076 6965 7773 206f 6620 everal views of \n+00007100: 6120 6379 6c69 6e64 7269 6361 6c0a 7072 a cylindrical.pr\n+00007110: 6973 6d20 666f 6c6c 6f77 732e 0a20 2064 ism follows.. d\n+00007120: 6566 206e 5f63 796c 5f73 6567 7320 3230 ef n_cyl_segs 20\n+00007130: 2020 6465 6620 6e5f 7669 6577 7320 3520 def n_views 5 \n+00007140: 2064 6566 2049 205b 312c 302c 305d 0a20 def I [1,0,0]. \n+00007150: 2064 6566 2065 6e64 6f70 7473 205b 6669 def endopts [fi\n+00007160: 6c6c 636f 6c6f 723d 6c69 6768 7467 7261 llcolor=lightgra\n+00007170: 795d 0a20 2072 6570 6561 7420 7b20 6e5f y]. repeat { n_\n+00007180: 7669 6577 732c 2072 6f74 6174 6528 3138 views, rotate(18\n+00007190: 302f 6e5f 7669 6577 732c 205b 495d 2920 0/n_views, [I]) \n+000071a0: 7468 656e 2074 7261 6e73 6c61 7465 285b then translate([\n+000071b0: 495d 202a 2032 2e31 2920 7d20 0a20 2020 I] * 2.1) } . \n+000071c0: 2073 7765 6570 5b65 6e64 6f70 7473 5d7b sweep[endopts]{\n+000071d0: 206e 5f63 796c 5f73 6567 733c 3e2c 2072 n_cyl_segs<>, r\n+000071e0: 6f74 6174 6528 3336 302f 6e5f 6379 6c5f otate(360/n_cyl_\n+000071f0: 7365 6773 2c20 5b30 2c31 2c30 5d29 207d segs, [0,1,0]) }\n+00007200: 200a 2020 2020 2020 6c69 6e65 5b66 696c . line[fil\n+00007210: 6c63 6f6c 6f72 3d77 6869 7465 5d28 312c lcolor=white](1,\n+00007220: 2d31 2928 312c 3129 0a49 7420 7072 6f64 -1)(1,1).It prod\n+00007230: 7563 6573 2074 6869 7320 6472 6177 696e uces this drawin\n+00007240: 672e 0a0a 0008 5b69 6d61 6765 2073 7263 g.....[image src\n+00007250: 3d22 6578 3131 302e 706e 6722 2074 6578 =\"ex110.png\" tex\n+00007260: 743d 2249 6d61 6765 2065 7831 3130 206f t=\"Image ex110 o\n+00007270: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n+00007280: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n+00007290: 6f63 756d 656e 742e 2200 085d 0a0a 5468 ocument.\"..]..Th\n+000072a0: 6520 6f70 7469 6f6e 7320 6f66 2074 6865 e options of the\n+000072b0: 2073 7765 7074 206c 696e 652c 2069 6620 swept line, if \n+000072c0: 616e 792c 2061 7265 2061 7070 6c69 6564 any, are applied\n+000072d0: 2074 6f20 7468 6520 6661 6365 7320 7072 to the faces pr\n+000072e0: 6f64 7563 6564 0a62 7920 7377 6565 7069 oduced.by sweepi\n+000072f0: 6e67 2074 6865 206c 696e 652c 2062 7574 ng the line, but\n+00007300: 206e 6f74 2074 6865 2065 6e64 2070 6f6c not the end pol\n+00007310: 7967 6f6e 732e 2020 4f74 6865 7277 6973 ygons. Otherwis\n+00007320: 652c 2074 6865 2073 7765 6570 0a6f 7074 e, the sweep.opt\n+00007330: 696f 6e73 2061 7265 2061 7070 6c69 6564 ions are applied\n+00007340: 2074 6872 6f75 6768 6f75 742e 2020 5468 throughout. Th\n+00007350: 6520 6465 6620 696e 2074 6869 7320 6578 e def in this ex\n+00007360: 616d 706c 6520 6973 2061 6e20 e280 9c6f ample is an ...o\n+00007370: 7074 696f 6ee2 809d 0a64 6566 696e 6974 ption....definit\n+00007380: 696f 6e2e 2020 5265 6665 7265 6e63 6573 ion. 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While not\n+00007560: 2061 7070 6172 656e 7420 696e 2074 6869 apparent in thi\n+00007570: 730a 6578 616d 706c 652c 206f 7074 696f s.example, optio\n+00007580: 6e73 2072 6566 6572 656e 6365 7320 6172 ns references ar\n+00007590: 6520 7573 6566 756c 2077 6865 6e20 6465 e useful when de\n+000075a0: 6669 6e69 6e67 206d 616e 7920 6f62 6a65 fining many obje\n+000075b0: 6374 7320 7769 7468 2061 0a73 696d 696c cts with a.simil\n+000075c0: 6172 2061 7070 6561 7261 6e63 652e 0a0a ar appearance...\n+000075d0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+000075e0: 6e66 6f2c 2020 4e6f 6465 3a20 4166 6669 nfo, Node: Affi\n+000075f0: 6e65 2061 7269 7468 6d65 7469 632c 2020 ne arithmetic, \n+00007600: 4e65 7874 3a20 4d6f 7265 2074 6f20 6c65 Next: More to le\n+00007610: 6172 6e2c 2020 5072 6576 3a20 506f 6c79 arn, Prev: Poly\n+00007620: 6c69 6e65 2073 7765 6570 7320 7769 7468 line sweeps with\n+00007630: 2063 6c6f 7375 7265 2c20 2055 703a 2053 closure, Up: S\n+00007640: 7765 7074 206f 626a 6563 7473 0a0a 322e wept objects..2.\n+00007650: 372e 3620 4166 6669 6e65 2061 7269 7468 7.6 Affine arith\n+00007660: 6d65 7469 630a 2d2d 2d2d 2d2d 2d2d 2d2d metic.----------\n+00007670: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a54 -------------..T\n+00007680: 6865 2061 7269 7468 6d65 7469 6320 5b49 he arithmetic [I\n+00007690: 5d20 2a20 322e 3120 6162 6f76 6520 6869 ] * 2.1 above hi\n+000076a0: 6e74 7320 6174 2061 206c 6172 6765 7220 nts at a larger \n+000076b0: 7472 7574 682e 2020 e280 9853 6b65 7463 truth. ...Sketc\n+000076c0: 68e2 8099 0a6f 7065 7261 746f 7273 2077 h....operators w\n+000076d0: 6f72 6b20 6f6e 2073 6361 6c61 7273 2c20 ork on scalars, \n+000076e0: 7665 6374 6f72 732c 2070 6f69 6e74 732c vectors, points,\n+000076f0: 2061 6e64 2074 7261 6e73 666f 726d 7320 and transforms \n+00007700: 6163 636f 7264 696e 6720 746f 0a74 6865 according to.the\n+00007710: 2067 656e 6572 616c 2072 756c 6573 206f general rules o\n+00007720: 6620 e280 9c61 6666 696e 6520 616c 6765 f ...affine alge\n+00007730: 6272 61e2 809d 2e20 2054 6869 7320 6361 bra.... This ca\n+00007740: 6e20 6265 2068 656c 7066 756c 2066 6f72 n be helpful for\n+00007750: 2073 6574 7469 6e67 0a75 7020 6469 6167 setting.up diag\n+00007760: 7261 6d73 2077 6974 6820 636f 6d70 7574 rams with comput\n+00007770: 6564 2067 656f 6d65 7472 792e 2020 466f ed geometry. Fo\n+00007780: 7220 6578 616d 706c 652c 2069 6620 796f r example, if yo\n+00007790: 7520 6861 7665 2074 7269 616e 676c 650a u have triangle.\n+000077a0: 7665 7274 6963 6573 2028 7031 2920 7468 vertices (p1) th\n+000077b0: 726f 7567 6820 2870 3329 2061 6e64 206e rough (p3) and n\n+000077c0: 6565 6420 746f 2064 7261 7720 6120 756e eed to draw a un\n+000077d0: 6974 206e 6f72 6d61 6c20 7665 6374 6f72 it normal vector\n+000077e0: 0a70 6f69 6e74 696e 6720 6f75 7420 6f66 .pointing out of\n+000077f0: 2074 6865 2063 656e 7465 7220 6f66 2074 the center of t\n+00007800: 6865 2074 7269 616e 676c 652c 2074 6869 he triangle, thi\n+00007810: 7320 636f 6465 2064 6f65 7320 7468 6520 s code does the \n+00007820: 7472 6963 6b2e 0a20 2064 6566 2070 3120 trick.. def p1 \n+00007830: 2831 2c30 2c30 2920 2064 6566 2070 3220 (1,0,0) def p2 \n+00007840: 2830 2c30 2e35 2c30 2920 2064 6566 2070 (0,0.5,0) def p\n+00007850: 3320 282d 302e 352c 2d31 2c32 290a 2020 3 (-0.5,-1,2). \n+00007860: 6465 6620 4f20 2830 2c30 2c30 290a 2020 def O (0,0,0). \n+00007870: 6465 6620 4e20 756e 6974 2820 2828 7033 def N unit( ((p3\n+00007880: 2920 2d20 2870 3229 2920 2a20 2828 7031 ) - (p2)) * ((p1\n+00007890: 2920 2d20 2870 3229 2920 290a 2020 6465 ) - (p2)) ). de\n+000078a0: 6620 6e31 2028 2870 3129 2d28 4f29 202b f n1 ((p1)-(O) +\n+000078b0: 2028 7032 292d 284f 2920 2b20 2870 3329 (p2)-(O) + (p3)\n+000078c0: 2d28 4f29 2920 2f20 3320 2b20 284f 290a -(O)) / 3 + (O).\n+000078d0: 2020 6465 6620 6e32 2028 6e31 292b 5b4e def n2 (n1)+[N\n+000078e0: 5d0a 2020 706f 6c79 676f 6e28 7031 2928 ]. polygon(p1)(\n+000078f0: 7032 2928 7033 290a 2020 6c69 6e65 5b61 p2)(p3). line[a\n+00007900: 7272 6f77 733d 2a2d 3e5d 286e 3129 286e rrows=*->](n1)(n\n+00007910: 3229 0a54 6865 2066 6972 7374 206c 696e 2).The first lin\n+00007920: 6520 636f 6d70 7574 6573 2074 6865 2063 e computes the c\n+00007930: 726f 7373 2070 726f 6475 6374 206f 6620 ross product of \n+00007940: 7477 6f20 6564 6765 2076 6563 746f 7273 two edge vectors\n+00007950: 206f 6620 7468 650a 7472 6961 6e67 6c65 of the.triangle\n+00007960: 2061 6e64 2073 6361 6c65 7320 6974 2074 and scales it t\n+00007970: 6f20 756e 6974 206c 656e 6774 682e 2020 o unit length. \n+00007980: 5468 6520 7365 636f 6e64 2063 6f6d 7075 The second compu\n+00007990: 7465 7320 7468 6520 6176 6572 6167 650a tes the average.\n+000079a0: 6f66 2074 6865 2076 6572 7469 6365 732e of the vertices.\n+000079b0: 2020 4e6f 7465 2074 6861 7420 7375 6274 Note that subt\n+000079c0: 7261 6374 696f 6e20 616e 6420 6164 6469 raction and addi\n+000079d0: 7469 6f6e 206f 6620 7468 6520 6f72 6967 tion of the orig\n+000079e0: 696e 0a65 6666 6563 7469 7665 6c79 2063 in.effectively c\n+000079f0: 6f6e 7665 7274 2076 6563 746f 7273 2074 onvert vectors t\n+00007a00: 6f20 706f 696e 7473 2061 6e64 205f 7669 o points and _vi\n+00007a10: 6365 2076 6572 7361 5f2e 2020 5468 6520 ce versa_. The \n+00007a20: 6c69 6e65 0a63 6f6d 6d61 6e64 2064 7261 line.command dra\n+00007a30: 7773 2074 6865 206e 6f72 6d61 6c20 6174 ws the normal at\n+00007a40: 2074 6865 2063 6f72 7265 6374 2073 706f the correct spo\n+00007a50: 742e 0a0a 0008 5b69 6d61 6765 2073 7263 t.....[image src\n+00007a60: 3d22 6578 3130 302e 706e 6722 2074 6578 =\"ex100.png\" tex\n+00007a70: 743d 2249 6d61 6765 2065 7831 3030 206f t=\"Image ex100 o\n+00007a80: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n+00007a90: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n+00007aa0: 6f63 756d 656e 742e 2200 085d 0a0a 2020 ocument.\"..].. \n+00007ab0: 2054 776f 2063 6176 6561 7473 2072 6567 Two caveats reg\n+00007ac0: 6172 6469 6e67 2074 6869 7320 6578 616d arding this exam\n+00007ad0: 706c 6520 7265 6d61 696e 2e20 2046 6972 ple remain. Fir\n+00007ae0: 7374 2c20 7468 6520 6f6e 6c79 2077 6179 st, the only way\n+00007af0: 2074 6f0a 7573 6520 e280 9850 5354 7269 to.use ...PSTri\n+00007b00: 636b 73e2 8099 2d73 7479 6c65 2061 7272 cks...-style arr\n+00007b10: 6f77 7320 6973 2077 6974 6820 6172 726f ows is with arro\n+00007b20: 7773 3d2e 2020 5468 6520 616c 7465 726e ws=. The altern\n+00007b30: 6174 6976 6520 7379 6e74 6178 2066 6f72 ative syntax for\n+00007b40: 0ae2 8098 5053 5472 6963 6b73 e280 9920 ....PSTricks... \n+00007b50: 6172 726f 7773 2069 7320 6e6f 7420 616c arrows is not al\n+00007b60: 6c6f 7765 6420 696e 2073 6b65 7463 682e lowed in sketch.\n+00007b70: 2020 5365 636f 6e64 2c20 796f 7520 6d69 Second, you mi\n+00007b80: 6768 7420 6c69 6b65 2074 6f0a 656c 696d ght like to.elim\n+00007b90: 696e 6174 6520 7468 6520 7468 6972 6420 inate the third \n+00007ba0: 6465 6620 616e 6420 7772 6974 6520 696e def and write in\n+00007bb0: 7374 6561 6420 7468 6520 666f 6c6c 6f77 stead the follow\n+00007bc0: 696e 672e 0a20 206c 696e 655b 6172 726f ing.. line[arro\n+00007bd0: 7773 3d2a 2d3e 5d28 6e31 2920 286e 3129 ws=*->](n1) (n1)\n+00007be0: 2b5b 4e5d 0a54 6869 7320 6973 206e 6f74 +[N].This is not\n+00007bf0: 2061 6c6c 6f77 6564 2e20 2054 6865 2070 allowed. 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\n+00007e10: 2057 6520 696e 7669 7465 2074 6865 2072 We invite the r\n+00007e20: 6561 6465 7220 696e 746f 0a74 6865 206d eader into.the m\n+00007e30: 6169 6e20 626f 6479 206f 6620 7468 6973 ain body of this\n+00007e40: 2064 6f63 756d 656e 7461 7469 6f6e 202a documentation *\n+00007e50: 6e6f 7465 2053 7765 6570 733a 3a20 746f note Sweeps:: to\n+00007e60: 206c 6561 726e 206d 6f72 652e 0a0a 0008 learn more.....\n+00007e70: 5b69 6d61 6765 2073 7263 3d22 6578 3132 [image src=\"ex12\n+00007e80: 302e 706e 6722 2074 6578 743d 2249 6d61 0.png\" text=\"Ima\n+00007e90: 6765 2065 7831 3230 206f 6d69 7474 6564 ge ex120 omitted\n+00007ea0: 2069 6e20 7465 7874 2076 6572 7369 6f6e in text version\n+00007eb0: 206f 6620 7468 6973 2064 6f63 756d 656e of this documen\n+00007ec0: 742e 2200 085d 0a0a 5768 6f20 6b6e 6f77 t.\"..]..Who know\n+00007ed0: 7320 7768 6572 6520 796f 7527 6c6c 2066 s where you'll f\n+00007ee0: 696e 6973 683f 0a0a 1f0a 4669 6c65 3a20 inish?....File: \n+00007ef0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+00007f00: 6465 3a20 496e 7075 7420 6c61 6e67 7561 de: Input langua\n+00007f10: 6765 2c20 204e 6578 743a 2042 7569 6c64 ge, Next: Build\n+00007f20: 696e 6720 6120 6472 6177 696e 672c 2020 ing a drawing, \n+00007f30: 5072 6576 3a20 496e 7472 6f64 7563 7469 Prev: Introducti\n+00007f40: 6f6e 2062 7920 6578 616d 706c 652c 2020 on by example, \n+00007f50: 5570 3a20 546f 700a 0a33 2049 6e70 7574 Up: Top..3 Input\n+00007f60: 206c 616e 6775 6167 650a 2a2a 2a2a 2a2a language.******\n+00007f70: 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a 5468 6973 **********..This\n+00007f80: 2063 6861 7074 6572 2064 6573 6372 6962 chapter describ\n+00007f90: 6573 2074 6865 20e2 8098 736b 6574 6368 es the ...sketch\n+00007fa0: e280 9920 696e 7075 7420 6c61 6e67 7561 ... input langua\n+00007fb0: 6765 2069 6e20 6465 7461 696c 2e0a 0a2a ge in detail...*\n+00007fc0: 204d 656e 753a 0a0a 2a20 4c61 6e67 7561 Menu:..* Langua\n+00007fd0: 6765 2062 6173 6963 733a 3a20 2020 2020 ge basics:: \n+00007fe0: 2020 2020 2020 2020 4361 7365 2c20 7370 Case, sp\n+00007ff0: 6163 652c 2063 6f6d 6d65 6e74 732c 2069 ace, comments, i\n+00008000: 6e63 6c75 6465 2066 696c 6573 2e0a 2a20 nclude files..* \n+00008010: 4472 6177 6162 6c65 733a 3a20 2020 2020 Drawables:: \n+00008020: 2020 2020 2020 2020 2020 2020 2020 5468 Th\n+00008030: 696e 6773 2074 6861 7420 6361 6e20 6265 ings that can be\n+00008040: 2064 7261 776e 2e0a 2a20 4465 6669 6e69 drawn..* Defini\n+00008050: 7469 6f6e 733a 3a20 2020 2020 2020 2020 tions:: \n+00008060: 2020 2020 2020 2020 4769 7669 6e67 2074 Giving t\n+00008070: 6869 6e67 7320 6e61 6d65 732e 0a2a 2047 hings names..* G\n+00008080: 6c6f 6261 6c20 656e 7669 726f 6e6d 656e lobal environmen\n+00008090: 743a 3a20 2020 2020 2020 2020 2041 6666 t:: Aff\n+000080a0: 6563 7420 7468 6520 656e 7469 7265 2064 ect the entire d\n+000080b0: 7261 7769 6e67 2e0a 0a1f 0a46 696c 653a rawing.....File:\n+000080c0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+000080d0: 6f64 653a 204c 616e 6775 6167 6520 6261 ode: Language ba\n+000080e0: 7369 6373 2c20 204e 6578 743a 2044 7261 sics, Next: Dra\n+000080f0: 7761 626c 6573 2c20 2050 7265 763a 2049 wables, Prev: I\n+00008100: 6e70 7574 206c 616e 6775 6167 652c 2020 nput language, \n+00008110: 5570 3a20 496e 7075 7420 6c61 6e67 7561 Up: Input langua\n+00008120: 6765 0a0a 332e 3120 4261 7369 6373 0a3d ge..3.1 Basics.=\n+00008130: 3d3d 3d3d 3d3d 3d3d 3d0a 0ae2 8098 536b =========.....Sk\n+00008140: 6574 6368 e280 9920 696e 7075 7420 6973 etch... input is\n+00008150: 2070 6c61 696e 2041 5343 4949 2074 6578 plain ASCII tex\n+00008160: 742c 2075 7375 616c 6c79 2073 746f 7265 t, usually store\n+00008170: 6420 696e 2061 6e20 696e 7075 7420 6669 d in an input fi\n+00008180: 6c65 2e20 2049 740a 6465 7363 7269 6265 le. 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The last ch\n+00008810: 6172 6163 7465 7220 6d61 7920 5f6e 6f74 aracter may _not\n+00008820: 5f20 6265 2061 6e20 756e 6465 7273 636f _ be an undersco\n+00008830: 7265 2e0a 4b65 7977 6f72 6473 2063 616e re..Keywords can\n+00008840: 6e6f 7420 6265 2075 7365 6420 6173 2069 not be used as i\n+00008850: 6465 6e74 6966 6965 7273 2c20 616e 6420 dentifiers, and \n+00008860: 7265 7365 7276 6564 2077 6f72 6473 206f reserved words o\n+00008870: 7567 6874 2074 6f20 6265 0a61 766f 6964 ught to be.avoid\n+00008880: 6564 2e20 202a 4e6f 7465 204b 6579 2061 ed. *Note Key a\n+00008890: 6e64 2072 6573 6572 7665 6420 776f 7264 nd reserved word\n+000088a0: 733a 3a2e 0a0a 1f0a 4669 6c65 3a20 736b s::.....File: sk\n+000088b0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+000088c0: 3a20 4b65 7920 616e 6420 7265 7365 7276 : Key and reserv\n+000088d0: 6564 2077 6f72 6473 2c20 204e 6578 743a ed words, Next:\n+000088e0: 204c 6974 6572 616c 732c 2020 5072 6576 Literals, Prev\n+000088f0: 3a20 4964 656e 7469 6669 6572 732c 2020 : Identifiers, \n+00008900: 5570 3a20 4c61 6e67 7561 6765 2062 6173 Up: Language bas\n+00008910: 6963 730a 0a33 2e31 2e32 204b 6579 2061 ics..3.1.2 Key a\n+00008920: 6e64 2072 6573 6572 7665 6420 776f 7264 nd reserved word\n+00008930: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d s.--------------\n+00008940: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a --------------..\n+00008950: 5468 6520 6b65 7977 6f72 6473 206f 6620 The keywords of \n+00008960: e280 9873 6b65 7463 68e2 8099 2061 7265 ...sketch... are\n+00008970: 20e2 8098 7069 6374 7572 6562 6f78 e280 ...picturebox..\n+00008980: 9920 e280 9863 7572 7665 e280 9920 e280 . ...curve... ..\n+00008990: 9864 6566 e280 9920 e280 9864 6f74 73e2 .def... ...dots.\n+000089a0: 8099 20e2 8098 6672 616d 65e2 8099 0ae2 .. ...frame.....\n+000089b0: 8098 676c 6f62 616c e280 9920 e280 9869 ..global... ...i\n+000089c0: 6e70 7574 e280 9920 e280 986c 696e 65e2 nput... ...line.\n+000089d0: 8099 20e2 8098 706f 6c79 676f 6ee2 8099 .. ...polygon...\n+000089e0: 20e2 8098 7075 74e2 8099 20e2 8098 7265 ...put... ...re\n+000089f0: 7065 6174 e280 9920 e280 9873 6574 e280 peat... ...set..\n+00008a00: 9920 e280 9873 7765 6570 e280 9920 616e . ...sweep... an\n+00008a10: 640a e280 9874 6865 6ee2 8099 2e20 2054 d....then.... 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The z\n+000090b0: 2d63 6f6d 706f 6e65 6e74 730a 6172 6520 -components.are \n+000090c0: 6f70 7469 6f6e 616c 2061 6e64 2064 6566 optional and def\n+000090d0: 6175 6c74 2074 6f20 7a65 726f 2e0a 0a1f ault to zero....\n+000090e0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+000090f0: 666f 2c20 204e 6f64 653a 2054 7261 6e73 fo, Node: Trans\n+00009100: 666f 726d 206c 6974 6572 616c 732c 2020 form literals, \n+00009110: 5072 6576 3a20 506f 696e 7420 616e 6420 Prev: Point and \n+00009120: 7665 6374 6f72 206c 6974 6572 616c 732c vector literals,\n+00009130: 2020 5570 3a20 4c69 7465 7261 6c73 0a0a Up: Literals..\n+00009140: 332e 312e 332e 3320 5472 616e 7366 6f72 3.1.3.3 Transfor\n+00009150: 6d20 6c69 7465 7261 6c73 0a2e 2e2e 2e2e m literals......\n 00009160: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-00009170: 2e2e 2e2e 2e2e 2e0a 0a4d 6f73 7420 7472 .........Most tr\n-00009180: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00009190: 2061 7265 2066 6f72 6d65 6420 6279 20e2 are formed by .\n-000091a0: 809c 636f 6e73 7472 7563 746f 7273 e280 ..constructors..\n-000091b0: 9d2e 2020 5468 6573 6520 6172 650a 7375 .. These are.su\n-000091c0: 6d6d 6172 697a 6564 2069 6e20 7468 6520 mmarized in the \n-000091d0: 666f 6c6c 6f77 696e 6720 7461 626c 652e following table.\n-000091e0: 0a43 6f6e 7374 7275 6374 6f72 2020 2020 .Constructor \n+00009170: 2e2e 2e2e 2e0a 0a4d 6f73 7420 7472 616e .......Most tran\n+00009180: 7366 6f72 6d20 6c69 7465 7261 6c73 2061 sform literals a\n+00009190: 7265 2066 6f72 6d65 6420 6279 20e2 809c re formed by ...\n+000091a0: 636f 6e73 7472 7563 746f 7273 e280 9d2e constructors....\n+000091b0: 2020 5468 6573 6520 6172 650a 7375 6d6d These are.summ\n+000091c0: 6172 697a 6564 2069 6e20 7468 6520 666f arized in the fo\n+000091d0: 6c6c 6f77 696e 6720 7461 626c 652e 0a43 llowing table..C\n+000091e0: 6f6e 7374 7275 6374 6f72 2020 2020 2020 onstructor \n 000091f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009200: 2020 2020 2050 6172 616d 2074 7970 6573 Param types\n-00009210: 2020 2020 2020 2020 2020 2044 6573 6372 Descr\n-00009220: 6970 7469 6f6e 0a2d 2d2d 2d2d 2d2d 2d2d 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degrees about po\n-000092f0: 696e 7420 e280 9850 e280 9920 7769 7468 int ...P... with\n-00009300: 2061 7869 730a 2020 2020 2020 2020 2020 axis. \n+00009290: 0ae2 8098 726f 7461 7465 2841 2c50 2c58 ....rotate(A,P,X\n+000092a0: 29e2 8099 2020 2020 2020 2020 2020 2020 )... \n+000092b0: 2020 2020 2020 2020 2073 6361 6c61 722c scalar,\n+000092c0: 706f 696e 742c 7665 6374 6f72 2020 2052 point,vector R\n+000092d0: 6f74 6174 6520 e280 9841 e280 9920 6465 otate ...A... de\n+000092e0: 6772 6565 7320 6162 6f75 7420 706f 696e grees about poin\n+000092f0: 7420 e280 9850 e280 9920 7769 7468 2061 t ...P... with a\n+00009300: 7869 730a 2020 2020 2020 2020 2020 2020 xis. \n 00009310: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009320: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009330: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009340: e280 9858 e280 9920 6163 636f 7264 696e ...X... accordin\n-00009350: 6720 746f 2074 6865 2072 6967 6874 2068 g to the right h\n-00009360: 616e 6420 7275 6c65 2e0a 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2020 2020 2020 2020 2020 2020 \n 000093f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009400: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009410: 2020 2020 206f 7074 696f 6e61 6c20 616e optional an\n-00009420: 6420 6465 6661 756c 7420 746f 2074 6865 d default to the\n-00009430: 206f 7269 6769 6e20 616e 6420 7468 650a origin and the.\n+00009410: 2020 206f 7074 696f 6e61 6c20 616e 6420 optional and \n+00009420: 6465 6661 756c 7420 746f 2074 6865 206f default to the o\n+00009430: 7269 6769 6e20 616e 6420 7468 650a 2020 rigin and the. \n 00009440: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009450: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00009460: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009470: 2020 2020 2020 2020 2020 7a2d 6178 6973 z-axis\n-00009480: 2072 6573 7065 6374 6976 656c 792e 0ae2 respectively...\n-00009490: 8098 7472 616e 736c 6174 6528 5829 e280 ..translate(X)..\n-000094a0: 9920 2020 2020 2020 2020 2020 2020 2020 . \n-000094b0: 2020 2020 2020 2076 6563 746f 7220 2020 vector \n-000094c0: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-000094d0: 6e73 6c61 7465 2062 7920 e280 9858 e280 nslate by ...X..\n-000094e0: 992e 0ae2 8098 7363 616c 6528 5329 e280 ......scale(S)..\n-000094f0: 9920 2020 2020 2020 2020 2020 2020 2020 . \n-00009500: 2020 2020 2020 2020 2020 2073 6361 6c61 scala\n-00009510: 7220 2020 2020 2020 2020 2020 2020 2020 r \n-00009520: 2053 6361 6c65 2075 6e69 666f 726d 6c79 Scale uniformly\n-00009530: 2062 7920 6661 6374 6f72 20e2 8098 53e2 by factor ...S.\n-00009540: 8099 2e0a e280 9873 6361 6c65 2856 29e2 .......scale(V).\n-00009550: 8099 2020 2020 2020 2020 2020 2020 2020 .. \n-00009560: 2020 2020 2020 2020 2020 2020 7665 6374 vect\n-00009570: 6f72 2020 2020 2020 2020 2020 2020 2020 or \n-00009580: 2020 5363 616c 6520 616c 6f6e 6720 6561 Scale along ea\n-00009590: 6368 2061 7869 7320 6279 2063 6f6d 706f ch axis by compo\n-000095a0: 6e65 6e74 7320 6f66 20e2 8098 56e2 8099 nents of ...V...\n-000095b0: 2e0a e280 9870 726f 6a65 6374 2829 e280 .....project()..\n-000095c0: 9920 2020 2020 2020 2020 2020 2020 2020 . \n-000095d0: 2020 2020 2020 2020 2020 2d2d 2020 2020 -- \n-000095e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000095f0: 5361 6d65 2061 7320 e280 9873 6361 6c65 Same as ...scale\n-00009600: 285b 312c 312c 305d 29e2 8099 2e0a e280 ([1,1,0]).......\n-00009610: 9870 726f 6a65 6374 2853 29e2 8099 2020 .project(S)... \n+00009470: 2020 2020 2020 2020 7a2d 6178 6973 2072 z-axis r\n+00009480: 6573 7065 6374 6976 656c 792e 0ae2 8098 espectively.....\n+00009490: 7472 616e 736c 6174 6528 5829 e280 9920 translate(X)... \n+000094a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000094b0: 2020 2020 2076 6563 746f 7220 2020 2020 vector \n+000094c0: 2020 2020 2020 2020 2020 2054 7261 6e73 Trans\n+000094d0: 6c61 7465 2062 7920 e280 9858 e280 992e late by ...X....\n+000094e0: 0ae2 8098 7363 616c 6528 5329 e280 9920 ....scale(S)... \n+000094f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00009500: 2020 2020 2020 2020 2073 6361 6c61 7220 scalar \n+00009510: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+00009520: 6361 6c65 2075 6e69 666f 726d 6c79 2062 cale uniformly b\n+00009530: 7920 6661 6374 6f72 20e2 8098 53e2 8099 y factor ...S...\n+00009540: 2e0a e280 9873 6361 6c65 2856 29e2 8099 .....scale(V)...\n+00009550: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00009560: 2020 2020 2020 2020 2020 7665 6374 6f72 vector\n+00009570: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00009580: 5363 616c 6520 616c 6f6e 6720 6561 6368 Scale along each\n+00009590: 2061 7869 7320 6279 2063 6f6d 706f 6e65 axis by compone\n+000095a0: 6e74 7320 6f66 20e2 8098 56e2 8099 2e0a nts of ...V.....\n+000095b0: e280 9870 726f 6a65 6374 2829 e280 9920 ...project()... \n+000095c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000095d0: 2020 2020 2020 2020 2d2d 2020 2020 2020 -- \n+000095e0: 2020 2020 2020 2020 2020 2020 2020 5361 Sa\n+000095f0: 6d65 2061 7320 e280 9873 6361 6c65 285b me as ...scale([\n+00009600: 312c 312c 305d 29e2 8099 2e0a e280 9870 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proj\n-000096c0: 6563 7469 6f6e 2070 6c61 6e65 207a 3d2d ection plane z=-\n-000096d0: e280 9853 e280 992e 0ae2 8098 7065 7273 ...S........pers\n-000096e0: 7065 6374 6976 6528 5329 e280 9920 2020 pective(S)... \n-000096f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00009700: 2073 6361 6c61 7220 2020 2020 2020 2020 scalar \n-00009710: 2020 2020 2020 2050 6572 7370 6563 7469 Perspecti\n-00009720: 7665 205f 7472 616e 7366 6f72 6d5f 2069 ve _transform_ i\n-00009730: 6465 6e74 6963 616c 2074 6f0a 2020 2020 dentical to. \n+000096a0: 2020 2020 2020 2020 2020 2020 2020 206f o\n+000096b0: 7269 6769 6e20 616e 6420 7072 6f6a 6563 rigin and projec\n+000096c0: 7469 6f6e 2070 6c61 6e65 207a 3d2d e280 tion plane z=-..\n+000096d0: 9853 e280 992e 0ae2 8098 7065 7273 7065 .S........perspe\n+000096e0: 6374 6976 6528 5329 e280 9920 2020 2020 ctive(S)... \n+000096f0: 2020 2020 2020 2020 2020 2020 2020 2073 s\n+00009700: 6361 6c61 7220 2020 2020 2020 2020 2020 calar \n+00009710: 2020 2020 2050 6572 7370 6563 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[a\n-0000a0d0: 5f7b 3431 7d2c 615f 7b34 327d 2c61 5f7b _{41},a_{42},a_{\n-0000a0e0: 3433 7d2c 615f 7b34 347d 5d5d e280 990a 43},a_{44}]]....\n-0000a0f0: 5468 6520 e280 9870 726f 6a65 6374 e280 The ...project..\n-0000a100: 9920 636f 6e73 7472 7563 746f 7220 6973 . constructor is\n-0000a110: 206e 6f74 2067 656e 6572 616c 6c79 2075 not generally u\n-0000a120: 7365 6675 6c20 6265 6361 7573 6520 6974 seful because it\n-0000a130: 2064 6566 6561 7473 0a68 6964 6465 6e20 defeats.hidden \n-0000a140: 7375 7266 6163 6520 7265 6d6f 7661 6c20 surface removal \n-0000a150: 6279 2063 6f6c 6c61 7073 696e 6720 7468 by collapsing th\n-0000a160: 6520 7363 656e 6520 6f6e 746f 2061 2073 e scene onto a s\n-0000a170: 696e 676c 6520 706c 616e 652e 2020 4974 ingle plane. It\n-0000a180: 0a69 7320 6120 7370 6563 6961 6c20 7075 .is a special pu\n-0000a190: 7270 6f73 6520 7472 616e 7366 6f72 6d20 rpose transform \n-0000a1a0: 666f 7220 6472 6177 696e 6720 7069 6374 for drawing pict\n-0000a1b0: 7572 6573 206f 6620 7363 656e 6573 2077 ures of scenes w\n-0000a1c0: 6865 7265 0a74 6872 6565 2d64 696d 656e here.three-dimen\n-0000a1d0: 7369 6f6e 616c 206f 626a 6563 7473 2061 sional objects a\n-0000a1e0: 7265 2062 6569 6e67 2070 726f 6a65 6374 re being project\n-0000a1f0: 6564 206f 6e74 6f20 706c 616e 6573 2e20 ed onto planes. \n-0000a200: 2053 6565 2c20 666f 720a 6578 616d 706c See, for.exampl\n-0000a210: 652c 202a 6e6f 7465 204f 7665 7276 6965 e, *note Overvie\n-0000a220: 773a 3a2e 0a0a 2020 2054 6865 2064 6972 w::... The dir\n-0000a230: 6563 7420 7472 616e 7366 6f72 6d20 636f ect transform co\n-0000a240: 6e73 7472 7563 746f 7220 616c 6c6f 7773 nstructor allows\n-0000a250: 2064 6972 6563 7420 656e 7472 7920 6f66 direct entry of\n-0000a260: 2061 2034 7834 0a74 7261 6e73 666f 726d a 4x4.transform\n-0000a270: 6174 696f 6e20 6d61 7472 6978 2e20 204d ation matrix. M\n-0000a280: 6f73 7420 3364 2067 7261 7068 6963 7320 ost 3d graphics \n-0000a290: 7379 7374 656d 732c 2069 6e63 6c75 6469 systems, includi\n-0000a2a0: 6e67 20e2 8098 736b 6574 6368 e280 992c ng ...sketch...,\n-0000a2b0: 0a75 7365 2034 2d64 696d 656e 7369 6f6e .use 4-dimension\n-0000a2c0: 616c 2068 6f6d 6f67 656e 656f 7573 2063 al homogeneous c\n-0000a2d0: 6f6f 7264 696e 6174 6573 2069 6e74 6572 oordinates inter\n-0000a2e0: 6e61 6c6c 792e 2020 5468 6573 6520 6172 nally. These ar\n-0000a2f0: 650a 7472 616e 7366 6f72 6d65 6420 6279 e.transformed by\n-0000a300: 206d 756c 7469 706c 6963 6174 696f 6e20 multiplication \n-0000a310: 7769 7468 2034 7834 206d 6174 7269 6365 with 4x4 matrice\n-0000a320: 732e 2020 5468 6520 6275 696c 742d 696e s. The built-in\n-0000a330: 0a63 6f6e 7374 7275 6374 6f72 7320 28e2 .constructors (.\n-0000a340: 8098 726f 7461 7465 e280 992c 20e2 8098 ..rotate..., ...\n-0000a350: 7363 616c 65e2 8099 2c20 6574 632e 2920 scale..., etc.) \n-0000a360: 2061 7265 2061 6c6c 2074 7261 6e73 6c61 are all transla\n-0000a370: 7465 6420 696e 7465 726e 616c 6c79 2074 ted internally t\n-0000a380: 6f0a 7375 6368 2034 7834 206d 6174 7269 o.such 4x4 matri\n-0000a390: 6365 732e 2020 466f 7220 6d6f 7265 2069 ces. For more i\n-0000a3a0: 6e66 6f72 6d61 7469 6f6e 206f 6e20 686f nformation on ho\n-0000a3b0: 6d6f 6765 6e65 6f75 7320 636f 6f72 6469 mogeneous coordi\n-0000a3c0: 6e61 7465 0a74 7261 6e73 666f 726d 6174 nate.transformat\n-0000a3d0: 696f 6e73 2c20 7365 6520 616e 7920 676f ions, see any go\n-0000a3e0: 6f64 2063 6f6d 7075 7465 7220 6772 6170 od computer grap\n-0000a3f0: 6869 6373 2074 6578 7462 6f6f 6b2e 2020 hics textbook. \n-0000a400: 5468 6520 6469 7265 6374 0a74 7261 6e73 The direct.trans\n-0000a410: 666f 726d 2066 6561 7475 7265 206f 6620 form feature of \n-0000a420: e280 9873 6b65 7463 68e2 8099 2061 6c6c ...sketch... all\n-0000a430: 6f77 7320 796f 7520 746f 2065 6e74 6572 ows you to enter\n-0000a440: 2061 206d 6174 7269 7820 6f66 2079 6f75 a matrix of you\n-0000a450: 7220 6f77 6e0a 6368 6f69 6365 2e20 2054 r own.choice. T\n-0000a460: 6865 7265 2061 7265 206e 6f74 206d 616e here are not man\n-0000a470: 7920 6361 7365 7320 7768 6572 6520 7468 y cases where th\n-0000a480: 6973 2069 7320 7573 6566 756c 2c20 6275 is is useful, bu\n-0000a490: 7420 6966 2079 6f75 2064 6f0a 6e65 6564 t if you do.need\n-0000a4a0: 2069 742c 2079 6f75 206e 6565 6420 6974 it, you need it\n-0000a4b0: 2062 6164 6c79 210a 0a1f 0a46 696c 653a badly!....File:\n-0000a4c0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-0000a4d0: 6f64 653a 2041 7269 7468 6d65 7469 632c ode: Arithmetic,\n-0000a4e0: 2020 4e65 7874 3a20 4f70 7469 6f6e 732c Next: Options,\n-0000a4f0: 2020 5072 6576 3a20 4c69 7465 7261 6c73 Prev: Literals\n-0000a500: 2c20 2055 703a 204c 616e 6775 6167 6520 , Up: Language \n-0000a510: 6261 7369 6373 0a0a 332e 312e 3420 4172 basics..3.1.4 Ar\n-0000a520: 6974 686d 6574 6963 2065 7870 7265 7373 ithmetic express\n-0000a530: 696f 6e73 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d ions.-----------\n-0000a540: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000a550: 2d0a 0a41 7269 7468 6d65 7469 6320 6578 -..Arithmetic ex\n-0000a560: 7072 6573 7369 6f6e 7320 6f76 6572 20e2 pressions over .\n-0000a570: 8098 736b 6574 6368 e280 9920 6c69 7465 ..sketch... lite\n-0000a580: 7261 6c73 2061 6e64 2064 6566 696e 6564 rals and defined\n-0000a590: 2069 6465 6e74 6966 6965 7273 0a61 7265 identifiers.are\n-0000a5a0: 2073 756d 6d61 7269 7a65 6420 696e 2074 summarized in t\n-0000a5b0: 6865 2066 6f6c 6c6f 7769 6e67 2074 6162 he following tab\n-0000a5c0: 6c65 732e 0a0a 2a20 4d65 6e75 3a0a 0a2a les...* Menu:..*\n-0000a5d0: 2054 776f 2d6f 7065 7261 6e64 2028 6269 Two-operand (bi\n-0000a5e0: 6e61 7279 2920 666f 726d 733a 3a20 2041 nary) forms:: A\n-0000a5f0: 206f 7020 420a 2a20 556e 6172 7920 666f op B.* Unary fo\n-0000a600: 726d 733a 3a20 2020 2020 2020 2020 2020 rms:: \n-0000a610: 2020 2020 2020 6f70 2041 2028 616e 6420 op A (and \n-0000a620: 6f74 6865 7273 290a 0a1f 0a46 696c 653a others)....File:\n-0000a630: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-0000a640: 6f64 653a 2054 776f 2d6f 7065 7261 6e64 ode: Two-operand\n-0000a650: 2028 6269 6e61 7279 2920 666f 726d 732c (binary) forms,\n-0000a660: 2020 4e65 7874 3a20 556e 6172 7920 666f Next: Unary fo\n-0000a670: 726d 732c 2020 5072 6576 3a20 4172 6974 rms, Prev: Arit\n-0000a680: 686d 6574 6963 2c20 2055 703a 2041 7269 hmetic, Up: Ari\n-0000a690: 7468 6d65 7469 630a 0a33 2e31 2e34 2e31 thmetic..3.1.4.1\n-0000a6a0: 2054 776f 2d6f 7065 7261 6e64 2028 6269 Two-operand (bi\n-0000a6b0: 6e61 7279 2920 666f 726d 7320 616e 6420 nary) forms and \n-0000a6c0: 7072 6563 6564 656e 6365 0a2e 2e2e 2e2e precedence......\n+0000a050: 7468 6520 615f 7b69 6a7d 2069 7320 6120 the a_{ij} is a \n+0000a060: 7363 616c 6172 2065 7870 7265 7373 696f scalar expressio\n+0000a070: 6e2e 2020 5365 6520 7465 7874 0ae2 8098 n. See text....\n+0000a080: 205b 615f 7b33 317d 2c61 5f7b 3332 7d2c [a_{31},a_{32},\n+0000a090: 615f 7b33 337d 2c61 5f7b 3334 7d5d e280 a_{33},a_{34}]..\n+0000a0a0: 9920 2020 2020 2020 2020 2020 2020 2020 . \n+0000a0b0: 2020 2020 2020 2020 2020 2066 6f72 2064 for d\n+0000a0c0: 6574 6169 6c73 2e0a e280 9820 5b61 5f7b etails..... [a_{\n+0000a0d0: 3431 7d2c 615f 7b34 327d 2c61 5f7b 3433 41},a_{42},a_{43\n+0000a0e0: 7d2c 615f 7b34 347d 5d5d e280 990a 5468 },a_{44}]]....Th\n+0000a0f0: 6520 e280 9870 726f 6a65 6374 e280 9920 e ...project... \n+0000a100: 636f 6e73 7472 7563 746f 7220 6973 206e constructor is n\n+0000a110: 6f74 2067 656e 6572 616c 6c79 2075 7365 ot generally use\n+0000a120: 6675 6c20 6265 6361 7573 6520 6974 2064 ful because it d\n+0000a130: 6566 6561 7473 0a68 6964 6465 6e20 7375 efeats.hidden su\n+0000a140: 7266 6163 6520 7265 6d6f 7661 6c20 6279 rface removal by\n+0000a150: 2063 6f6c 6c61 7073 696e 6720 7468 6520 collapsing the \n+0000a160: 7363 656e 6520 6f6e 746f 2061 2073 696e scene onto a sin\n+0000a170: 676c 6520 706c 616e 652e 2020 4974 0a69 gle plane. It.i\n+0000a180: 7320 6120 7370 6563 6961 6c20 7075 7270 s a special purp\n+0000a190: 6f73 6520 7472 616e 7366 6f72 6d20 666f ose transform fo\n+0000a1a0: 7220 6472 6177 696e 6720 7069 6374 7572 r drawing pictur\n+0000a1b0: 6573 206f 6620 7363 656e 6573 2077 6865 es of scenes whe\n+0000a1c0: 7265 0a74 6872 6565 2d64 696d 656e 7369 re.three-dimensi\n+0000a1d0: 6f6e 616c 206f 626a 6563 7473 2061 7265 onal objects are\n+0000a1e0: 2062 6569 6e67 2070 726f 6a65 6374 6564 being projected\n+0000a1f0: 206f 6e74 6f20 706c 616e 6573 2e20 2053 onto planes. S\n+0000a200: 6565 2c20 666f 720a 6578 616d 706c 652c ee, for.example,\n+0000a210: 202a 6e6f 7465 204f 7665 7276 6965 773a *note Overview:\n+0000a220: 3a2e 0a0a 2020 2054 6865 2064 6972 6563 :... The direc\n+0000a230: 7420 7472 616e 7366 6f72 6d20 636f 6e73 t transform cons\n+0000a240: 7472 7563 746f 7220 616c 6c6f 7773 2064 tructor allows d\n+0000a250: 6972 6563 7420 656e 7472 7920 6f66 2061 irect entry of a\n+0000a260: 2034 7834 0a74 7261 6e73 666f 726d 6174 4x4.transformat\n+0000a270: 696f 6e20 6d61 7472 6978 2e20 204d 6f73 ion matrix. Mos\n+0000a280: 7420 3364 2067 7261 7068 6963 7320 7379 t 3d graphics sy\n+0000a290: 7374 656d 732c 2069 6e63 6c75 6469 6e67 stems, including\n+0000a2a0: 20e2 8098 736b 6574 6368 e280 992c 0a75 ...sketch...,.u\n+0000a2b0: 7365 2034 2d64 696d 656e 7369 6f6e 616c se 4-dimensional\n+0000a2c0: 2068 6f6d 6f67 656e 656f 7573 2063 6f6f homogeneous coo\n+0000a2d0: 7264 696e 6174 6573 2069 6e74 6572 6e61 rdinates interna\n+0000a2e0: 6c6c 792e 2020 5468 6573 6520 6172 650a lly. These are.\n+0000a2f0: 7472 616e 7366 6f72 6d65 6420 6279 206d transformed by m\n+0000a300: 756c 7469 706c 6963 6174 696f 6e20 7769 ultiplication wi\n+0000a310: 7468 2034 7834 206d 6174 7269 6365 732e th 4x4 matrices.\n+0000a320: 2020 5468 6520 6275 696c 742d 696e 0a63 The built-in.c\n+0000a330: 6f6e 7374 7275 6374 6f72 7320 28e2 8098 onstructors (...\n+0000a340: 726f 7461 7465 e280 992c 20e2 8098 7363 rotate..., ...sc\n+0000a350: 616c 65e2 8099 2c20 6574 632e 2920 2061 ale..., etc.) a\n+0000a360: 7265 2061 6c6c 2074 7261 6e73 6c61 7465 re all translate\n+0000a370: 6420 696e 7465 726e 616c 6c79 2074 6f0a d internally to.\n+0000a380: 7375 6368 2034 7834 206d 6174 7269 6365 such 4x4 matrice\n+0000a390: 732e 2020 466f 7220 6d6f 7265 2069 6e66 s. For more inf\n+0000a3a0: 6f72 6d61 7469 6f6e 206f 6e20 686f 6d6f ormation on homo\n+0000a3b0: 6765 6e65 6f75 7320 636f 6f72 6469 6e61 geneous coordina\n+0000a3c0: 7465 0a74 7261 6e73 666f 726d 6174 696f te.transformatio\n+0000a3d0: 6e73 2c20 7365 6520 616e 7920 676f 6f64 ns, see any good\n+0000a3e0: 2063 6f6d 7075 7465 7220 6772 6170 6869 computer graphi\n+0000a3f0: 6373 2074 6578 7462 6f6f 6b2e 2020 5468 cs textbook. Th\n+0000a400: 6520 6469 7265 6374 0a74 7261 6e73 666f e direct.transfo\n+0000a410: 726d 2066 6561 7475 7265 206f 6620 e280 rm feature of ..\n+0000a420: 9873 6b65 7463 68e2 8099 2061 6c6c 6f77 .sketch... allow\n+0000a430: 7320 796f 7520 746f 2065 6e74 6572 2061 s you to enter a\n+0000a440: 206d 6174 7269 7820 6f66 2079 6f75 7220 matrix of your \n+0000a450: 6f77 6e0a 6368 6f69 6365 2e20 2054 6865 own.choice. The\n+0000a460: 7265 2061 7265 206e 6f74 206d 616e 7920 re are not many \n+0000a470: 6361 7365 7320 7768 6572 6520 7468 6973 cases where this\n+0000a480: 2069 7320 7573 6566 756c 2c20 6275 7420 is useful, but \n+0000a490: 6966 2079 6f75 2064 6f0a 6e65 6564 2069 if you do.need i\n+0000a4a0: 742c 2079 6f75 206e 6565 6420 6974 2062 t, you need it b\n+0000a4b0: 6164 6c79 210a 0a1f 0a46 696c 653a 2073 adly!....File: s\n+0000a4c0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+0000a4d0: 653a 2041 7269 7468 6d65 7469 632c 2020 e: Arithmetic, \n+0000a4e0: 4e65 7874 3a20 4f70 7469 6f6e 732c 2020 Next: Options, \n+0000a4f0: 5072 6576 3a20 4c69 7465 7261 6c73 2c20 Prev: Literals, \n+0000a500: 2055 703a 204c 616e 6775 6167 6520 6261 Up: Language ba\n+0000a510: 7369 6373 0a0a 332e 312e 3420 4172 6974 sics..3.1.4 Arit\n+0000a520: 686d 6574 6963 2065 7870 7265 7373 696f hmetic expressio\n+0000a530: 6e73 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ns.-------------\n+0000a540: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ---------------.\n+0000a550: 0a41 7269 7468 6d65 7469 6320 6578 7072 .Arithmetic expr\n+0000a560: 6573 7369 6f6e 7320 6f76 6572 20e2 8098 essions over ...\n+0000a570: 736b 6574 6368 e280 9920 6c69 7465 7261 sketch... litera\n+0000a580: 6c73 2061 6e64 2064 6566 696e 6564 2069 ls and defined i\n+0000a590: 6465 6e74 6966 6965 7273 0a61 7265 2073 dentifiers.are s\n+0000a5a0: 756d 6d61 7269 7a65 6420 696e 2074 6865 ummarized in the\n+0000a5b0: 2066 6f6c 6c6f 7769 6e67 2074 6162 6c65 following table\n+0000a5c0: 732e 0a0a 2a20 4d65 6e75 3a0a 0a2a 2054 s...* Menu:..* T\n+0000a5d0: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n+0000a5e0: 7279 2920 666f 726d 733a 3a20 2041 206f ry) forms:: A o\n+0000a5f0: 7020 420a 2a20 556e 6172 7920 666f 726d p B.* Unary form\n+0000a600: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n+0000a610: 2020 2020 6f70 2041 2028 616e 6420 6f74 op A (and ot\n+0000a620: 6865 7273 290a 0a1f 0a46 696c 653a 2073 hers)....File: s\n+0000a630: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+0000a640: 653a 2054 776f 2d6f 7065 7261 6e64 2028 e: Two-operand (\n+0000a650: 6269 6e61 7279 2920 666f 726d 732c 2020 binary) forms, \n+0000a660: 4e65 7874 3a20 556e 6172 7920 666f 726d Next: Unary form\n+0000a670: 732c 2020 5072 6576 3a20 4172 6974 686d s, Prev: Arithm\n+0000a680: 6574 6963 2c20 2055 703a 2041 7269 7468 etic, Up: Arith\n+0000a690: 6d65 7469 630a 0a33 2e31 2e34 2e31 2054 metic..3.1.4.1 T\n+0000a6a0: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n+0000a6b0: 7279 2920 666f 726d 7320 616e 6420 7072 ry) forms and pr\n+0000a6c0: 6563 6564 656e 6365 0a2e 2e2e 2e2e 2e2e ecedence........\n 0000a6d0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n 0000a6e0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000a6f0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 4d6f ..............Mo\n-0000a700: 7374 2074 776f 2d6f 7065 7261 6e64 2062 st two-operand b\n-0000a710: 696e 6172 7920 666f 726d 7320 6861 7665 inary forms have\n-0000a720: 206d 6561 6e69 6e67 7320 6465 7065 6e64 meanings depend\n-0000a730: 656e 7420 6f6e 2074 6865 2074 7970 6573 ent on the types\n-0000a740: 206f 660a 7468 6569 7220 6172 6775 6d65 of.their argume\n-0000a750: 6e74 732e 2020 416e 2065 7868 6175 7374 nts. An exhaust\n-0000a760: 6976 6520 7375 6d6d 6172 7920 6f66 2074 ive summary of t\n-0000a770: 6865 2070 6f73 7369 6269 6c69 7469 6573 he possibilities\n-0000a780: 2069 7320 6769 7665 6e20 696e 0a74 6865 is given in.the\n-0000a790: 2066 6f6c 6c6f 7769 6e67 2074 6162 6c65 following table\n-0000a7a0: 2e0a 4c65 6674 2020 2020 2020 2020 4f70 ..Left Op\n-0000a7b0: 2020 2020 2020 2052 6967 6874 2020 2020 Right \n-0000a7c0: 2020 2052 6573 756c 7420 2020 2020 2044 Result D\n-0000a7d0: 6573 6372 6970 7469 6f6e 0a2d 2d2d 2d2d escription.-----\n+0000a6f0: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 4d6f 7374 ............Most\n+0000a700: 2074 776f 2d6f 7065 7261 6e64 2062 696e two-operand bin\n+0000a710: 6172 7920 666f 726d 7320 6861 7665 206d ary forms have m\n+0000a720: 6561 6e69 6e67 7320 6465 7065 6e64 656e eanings dependen\n+0000a730: 7420 6f6e 2074 6865 2074 7970 6573 206f t on the types o\n+0000a740: 660a 7468 6569 7220 6172 6775 6d65 6e74 f.their argument\n+0000a750: 732e 2020 416e 2065 7868 6175 7374 6976 s. An exhaustiv\n+0000a760: 6520 7375 6d6d 6172 7920 6f66 2074 6865 e summary of the\n+0000a770: 2070 6f73 7369 6269 6c69 7469 6573 2069 possibilities i\n+0000a780: 7320 6769 7665 6e20 696e 0a74 6865 2066 s given in.the f\n+0000a790: 6f6c 6c6f 7769 6e67 2074 6162 6c65 2e0a ollowing table..\n+0000a7a0: 4c65 6674 2020 2020 2020 2020 4f70 2020 Left Op \n+0000a7b0: 2020 2020 2052 6967 6874 2020 2020 2020 Right \n+0000a7c0: 2052 6573 756c 7420 2020 2020 2044 6573 Result Des\n+0000a7d0: 6372 6970 7469 6f6e 0a2d 2d2d 2d2d 2d2d cription.-------\n 0000a7e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a7f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a800: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a810: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a820: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000a830: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000a840: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000a850: 2d0a 7363 616c 6172 2020 2020 2020 e280 -.scalar ..\n-0000a860: 982b e280 9920 2020 2020 2073 6361 6c61 .+... scala\n-0000a870: 7220 2020 2020 2073 6361 6c61 7220 2020 r scalar \n-0000a880: 2020 2053 6361 6c61 7220 7375 6d2e 0a76 Scalar sum..v\n-0000a890: 6563 746f 7220 2020 2020 20e2 8098 2be2 ector ...+.\n-0000a8a0: 8099 2020 2020 2020 7665 6374 6f72 2020 .. vector \n-0000a8b0: 2020 2020 7665 6374 6f72 2020 2020 2020 vector \n-0000a8c0: 5665 6374 6f72 2073 756d 2e0a 706f 696e Vector sum..poin\n-0000a8d0: 7420 2020 2020 2020 e280 982b e280 9920 t ...+... \n-0000a8e0: 2020 2020 2076 6563 746f 7220 2020 2020 vector \n-0000a8f0: 2070 6f69 6e74 2020 2020 2020 2050 6f69 point Poi\n-0000a900: 6e74 2d76 6563 746f 7220 6166 6669 6e65 nt-vector affine\n-0000a910: 2073 756d 2e0a 7665 6374 6f72 2020 2020 sum..vector \n-0000a920: 2020 e280 982b e280 9920 2020 2020 2070 ...+... p\n-0000a930: 6f69 6e74 2020 2020 2020 2022 2020 2020 oint \" \n-0000a940: 2020 2020 2020 2022 0a73 6361 6c61 7220 \".scalar \n-0000a950: 2020 2020 20e2 8098 2de2 8099 2020 2020 ...-... \n-0000a960: 2020 7363 616c 6172 2020 2020 2020 7363 scalar sc\n-0000a970: 616c 6172 2020 2020 2020 5363 616c 6172 alar Scalar\n-0000a980: 2064 6966 6665 7265 6e63 652e 0a76 6563 difference..vec\n-0000a990: 746f 7220 2020 2020 20e2 8098 2de2 8099 tor ...-...\n-0000a9a0: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n-0000a9b0: 2020 7665 6374 6f72 2020 2020 2020 5665 vector Ve\n-0000a9c0: 6374 6f72 2064 6966 6665 7265 6e63 652e ctor difference.\n-0000a9d0: 0a70 6f69 6e74 2020 2020 2020 20e2 8098 .point ...\n-0000a9e0: 2de2 8099 2020 2020 2020 706f 696e 7420 -... point \n-0000a9f0: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n-0000aa00: 2020 506f 696e 742d 706f 696e 7420 6166 Point-point af\n-0000aa10: 6669 6e65 2064 6966 6665 7265 6e63 652e fine difference.\n-0000aa20: 0a70 6f69 6e74 2020 2020 2020 20e2 8098 .point ...\n-0000aa30: 2de2 8099 2020 2020 2020 7665 6374 6f72 -... vector\n-0000aa40: 2020 2020 2020 706f 696e 7420 2020 2020 point \n-0000aa50: 2020 506f 696e 742d 7665 6374 6f72 2061 Point-vector a\n-0000aa60: 6666 696e 6520 6469 6666 6572 656e 6365 ffine difference\n-0000aa70: 2e0a 7363 616c 6172 2020 2020 2020 e280 ..scalar ..\n-0000aa80: 982a e280 9920 6f72 2020 2073 6361 6c61 .*... or scala\n-0000aa90: 7220 2020 2020 2073 6361 6c61 7220 2020 r scalar \n-0000aaa0: 2020 2053 6361 6c61 7220 7072 6f64 7563 Scalar produc\n-0000aab0: 742e 0a20 2020 2020 2020 2020 2020 20e2 t.. .\n-0000aac0: 8098 2ee2 8099 0a73 6361 6c61 7220 2020 .......scalar \n-0000aad0: 2020 20e2 8098 2ae2 8099 206f 7220 2020 ...*... or \n-0000aae0: 7665 6374 6f72 2020 2020 2020 7665 6374 vector vect\n-0000aaf0: 6f72 2020 2020 2020 5363 616c 6172 2d76 or Scalar-v\n-0000ab00: 6563 746f 7220 7072 6f64 7563 742e 0a20 ector product.. \n-0000ab10: 2020 2020 2020 2020 2020 20e2 8098 2ee2 .....\n-0000ab20: 8099 0a76 6563 746f 7220 2020 2020 20e2 ...vector .\n-0000ab30: 8098 2ae2 8099 206f 7220 2020 7363 616c ..*... or scal\n-0000ab40: 6172 2020 2020 2020 2220 2020 2020 2020 ar \" \n-0000ab50: 2020 2020 220a 2020 2020 2020 2020 2020 \". \n-0000ab60: 2020 e280 982e e280 990a 7665 6374 6f72 ........vector\n-0000ab70: 2020 2020 2020 e280 982a e280 9920 2020 ...*... \n-0000ab80: 2020 2076 6563 746f 7220 2020 2020 2076 vector v\n-0000ab90: 6563 746f 7220 2020 2020 2056 6563 746f ector Vecto\n-0000aba0: 7220 6372 6f73 732d 7072 6f64 7563 742e r cross-product.\n-0000abb0: 0a76 6563 746f 7220 2020 2020 20e2 8098 .vector ...\n-0000abc0: 2ee2 8099 2020 2020 2020 7665 6374 6f72 .... vector\n-0000abd0: 2020 2020 2020 7363 616c 6172 2020 2020 scalar \n-0000abe0: 2020 5665 6374 6f72 2064 6f74 2070 726f Vector dot pro\n-0000abf0: 6475 6374 2e0a 7363 616c 6172 2020 2020 duct..scalar \n-0000ac00: 2020 e280 985e e280 9920 2020 2020 2073 ...^... s\n-0000ac10: 6361 6c61 7220 2020 2020 2073 6361 6c61 calar scala\n-0000ac20: 7220 2020 2020 2052 6169 7365 2073 6361 r Raise sca\n-0000ac30: 6c61 7220 746f 2073 6361 6c61 7220 706f lar to scalar po\n-0000ac40: 7765 722e 0a74 7261 6e73 666f 726d 2020 wer..transform \n-0000ac50: 20e2 8098 5ee2 8099 2020 2020 2020 696e ...^... in\n-0000ac60: 7465 6765 7220 2020 2020 7472 616e 7366 teger transf\n-0000ac70: 6f72 6d20 2020 5261 6973 6520 7472 616e orm Raise tran\n-0000ac80: 7366 6f72 6d20 746f 2069 6e74 6567 6572 sform to integer\n-0000ac90: 2070 6f77 6572 2e0a 7472 616e 7366 6f72 power..transfor\n-0000aca0: 6d20 2020 e280 982a e280 9920 6f72 2020 m ...*... or \n-0000acb0: 2070 6f69 6e74 2020 2020 2020 2070 6f69 point poi\n-0000acc0: 6e74 2020 2020 2020 2041 6666 696e 6520 nt Affine \n-0000acd0: 706f 696e 7420 7472 616e 7366 6f72 6d20 point transform \n-0000ace0: 2872 6967 6874 2d74 6f2d 6c65 6674 292e (right-to-left).\n-0000acf0: 0a20 2020 2020 2020 2020 2020 20e2 8098 . ...\n-0000ad00: 2ee2 8099 0a74 7261 6e73 666f 726d 2020 .....transform \n-0000ad10: 20e2 8098 2ae2 8099 206f 7220 2020 7665 ...*... or ve\n-0000ad20: 6374 6f72 2020 2020 2020 7665 6374 6f72 ctor vector\n-0000ad30: 2020 2020 2020 4166 6669 6e65 2076 6563 Affine vec\n-0000ad40: 746f 7220 7472 616e 7366 6f72 6d20 2872 tor transform (r\n-0000ad50: 6967 6874 2d74 6f2d 6c65 6674 292e 0a20 ight-to-left).. \n-0000ad60: 2020 2020 2020 2020 2020 20e2 8098 2ee2 .....\n-0000ad70: 8099 0a74 7261 6e73 666f 726d 2020 20e2 ...transform .\n-0000ad80: 8098 2ae2 8099 206f 7220 2020 7472 616e ..*... or tran\n-0000ad90: 7366 6f72 6d20 2020 7472 616e 7366 6f72 sform transfor\n-0000ada0: 6d20 2020 5472 616e 7366 6f72 6d20 636f m Transform co\n-0000adb0: 6d70 6f73 6974 696f 6e20 2872 6967 6874 mposition (right\n-0000adc0: 2d74 6f2d 6c65 6674 292e 0a20 2020 2020 -to-left).. \n-0000add0: 2020 2020 2020 20e2 8098 2ee2 8099 0a70 ........p\n-0000ade0: 6f69 6e74 2020 2020 2020 20e2 8098 7468 oint ...th\n-0000adf0: 656e e280 9920 2020 7472 616e 7366 6f72 en... transfor\n-0000ae00: 6d20 2020 706f 696e 7420 2020 2020 2020 m point \n-0000ae10: 4166 6669 6e65 2070 6f69 6e74 2074 7261 Affine point tra\n-0000ae20: 6e73 666f 726d 2028 6c65 6674 2d74 6f2d nsform (left-to-\n-0000ae30: 7269 6768 7429 2e0a 7665 6374 6f72 2020 right)..vector \n-0000ae40: 2020 2020 e280 9874 6865 6ee2 8099 2020 ...then... \n-0000ae50: 2074 7261 6e73 666f 726d 2020 2076 6563 transform vec\n-0000ae60: 746f 7220 2020 2020 2041 6666 696e 6520 tor Affine \n-0000ae70: 7665 6374 6f72 2074 7261 6e73 666f 726d vector transform\n-0000ae80: 2028 6c65 6674 2d74 6f2d 7269 6768 7429 (left-to-right)\n-0000ae90: 2e0a 7472 616e 7366 6f72 6d20 2020 e280 ..transform ..\n-0000aea0: 9874 6865 6ee2 8099 2020 2074 7261 6e73 .then... trans\n-0000aeb0: 666f 726d 2020 2074 7261 6e73 666f 726d form transform\n-0000aec0: 2020 2054 7261 6e73 666f 726d 2063 6f6d Transform com\n-0000aed0: 706f 7369 7469 6f6e 2028 6c65 6674 2d74 position (left-t\n-0000aee0: 6f2d 7269 6768 7429 2e0a 7363 616c 6172 o-right)..scalar\n-0000aef0: 2020 2020 2020 e280 982f e280 9920 2020 .../... \n-0000af00: 2020 2073 6361 6c61 7220 2020 2020 2073 scalar s\n-0000af10: 6361 6c61 7220 2020 2020 2053 6361 6c61 calar Scala\n-0000af20: 7220 6469 7669 7369 6f6e 2e0a 7665 6374 r division..vect\n-0000af30: 6f72 2020 2020 2020 e280 982f e280 9920 or .../... \n-0000af40: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n-0000af50: 2076 6563 746f 7220 2020 2020 2056 6563 vector Vec\n-0000af60: 746f 7220 636f 6d70 6f6e 656e 742d 7769 tor component-wi\n-0000af70: 7365 2064 6976 6973 696f 6e20 6279 2073 se division by s\n-0000af80: 6361 6c61 722e 0a70 6f69 6e74 2020 2020 calar..point \n-0000af90: 2020 20e2 8098 27e2 8099 2020 2020 2020 ...'... \n-0000afa0: e280 9878 e280 992c 20e2 8098 79e2 8099 ...x..., ...y...\n-0000afb0: 2c20 2020 7363 616c 6172 2020 2020 2020 , scalar \n-0000afc0: 506f 696e 7420 636f 6d70 6f6e 656e 7420 Point component \n-0000afd0: 6578 7472 6163 7469 6f6e 2e0a 2020 2020 extraction.. \n-0000afe0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000aff0: 206f 7220 e280 987a e280 990a 7665 6374 or ...z....vect\n-0000b000: 6f72 2020 2020 2020 e280 9827 e280 9920 or ...'... \n-0000b010: 2020 2020 20e2 8098 78e2 8099 2c20 e280 ...x..., ..\n-0000b020: 9879 e280 992c 2020 2073 6361 6c61 7220 .y..., scalar \n-0000b030: 2020 2020 2056 6563 746f 7220 636f 6d70 Vector comp\n-0000b040: 6f6e 656e 7420 6578 7472 6163 7469 6f6e onent extraction\n-0000b050: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n-0000b060: 2020 2020 2020 206f 7220 e280 987a e280 or ...z..\n-0000b070: 990a 0a4f 7065 7261 746f 7220 7072 6563 ...Operator prec\n-0000b080: 6564 656e 6365 2069 7320 7368 6f77 6e20 edence is shown \n-0000b090: 696e 2074 6869 7320 7461 626c 652e 0a4f in this table..O\n-0000b0a0: 7020 2020 2020 2020 5072 6563 6564 656e p Preceden\n-0000b0b0: 6365 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ce.-------------\n+0000a840: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ---------------.\n+0000a850: 7363 616c 6172 2020 2020 2020 e280 982b scalar ...+\n+0000a860: e280 9920 2020 2020 2073 6361 6c61 7220 ... scalar \n+0000a870: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n+0000a880: 2053 6361 6c61 7220 7375 6d2e 0a76 6563 Scalar sum..vec\n+0000a890: 746f 7220 2020 2020 20e2 8098 2be2 8099 tor ...+...\n+0000a8a0: 2020 2020 2020 7665 6374 6f72 2020 2020 vector \n+0000a8b0: 2020 7665 6374 6f72 2020 2020 2020 5665 vector Ve\n+0000a8c0: 6374 6f72 2073 756d 2e0a 706f 696e 7420 ctor sum..point \n+0000a8d0: 2020 2020 2020 e280 982b e280 9920 2020 ...+... \n+0000a8e0: 2020 2076 6563 746f 7220 2020 2020 2070 vector p\n+0000a8f0: 6f69 6e74 2020 2020 2020 2050 6f69 6e74 oint Point\n+0000a900: 2d76 6563 746f 7220 6166 6669 6e65 2073 -vector affine s\n+0000a910: 756d 2e0a 7665 6374 6f72 2020 2020 2020 um..vector \n+0000a920: e280 982b e280 9920 2020 2020 2070 6f69 ...+... poi\n+0000a930: 6e74 2020 2020 2020 2022 2020 2020 2020 nt \" \n+0000a940: 2020 2020 2022 0a73 6361 6c61 7220 2020 \".scalar \n+0000a950: 2020 20e2 8098 2de2 8099 2020 2020 2020 ...-... \n+0000a960: 7363 616c 6172 2020 2020 2020 7363 616c scalar scal\n+0000a970: 6172 2020 2020 2020 5363 616c 6172 2064 ar Scalar d\n+0000a980: 6966 6665 7265 6e63 652e 0a76 6563 746f ifference..vecto\n+0000a990: 7220 2020 2020 20e2 8098 2de2 8099 2020 r ...-... \n+0000a9a0: 2020 2020 7665 6374 6f72 2020 2020 2020 vector \n+0000a9b0: 7665 6374 6f72 2020 2020 2020 5665 6374 vector Vect\n+0000a9c0: 6f72 2064 6966 6665 7265 6e63 652e 0a70 or difference..p\n+0000a9d0: 6f69 6e74 2020 2020 2020 20e2 8098 2de2 oint ...-.\n+0000a9e0: 8099 2020 2020 2020 706f 696e 7420 2020 .. point \n+0000a9f0: 2020 2020 7665 6374 6f72 2020 2020 2020 vector \n+0000aa00: 506f 696e 742d 706f 696e 7420 6166 6669 Point-point affi\n+0000aa10: 6e65 2064 6966 6665 7265 6e63 652e 0a70 ne difference..p\n+0000aa20: 6f69 6e74 2020 2020 2020 20e2 8098 2de2 oint ...-.\n+0000aa30: 8099 2020 2020 2020 7665 6374 6f72 2020 .. vector \n+0000aa40: 2020 2020 706f 696e 7420 2020 2020 2020 point \n+0000aa50: 506f 696e 742d 7665 6374 6f72 2061 6666 Point-vector aff\n+0000aa60: 696e 6520 6469 6666 6572 656e 6365 2e0a ine difference..\n+0000aa70: 7363 616c 6172 2020 2020 2020 e280 982a scalar ...*\n+0000aa80: e280 9920 6f72 2020 2073 6361 6c61 7220 ... or scalar \n+0000aa90: 2020 2020 2073 6361 6c61 7220 2020 2020 scalar \n+0000aaa0: 2053 6361 6c61 7220 7072 6f64 7563 742e Scalar product.\n+0000aab0: 0a20 2020 2020 2020 2020 2020 20e2 8098 . ...\n+0000aac0: 2ee2 8099 0a73 6361 6c61 7220 2020 2020 .....scalar \n+0000aad0: 20e2 8098 2ae2 8099 206f 7220 2020 7665 ...*... or ve\n+0000aae0: 6374 6f72 2020 2020 2020 7665 6374 6f72 ctor vector\n+0000aaf0: 2020 2020 2020 5363 616c 6172 2d76 6563 Scalar-vec\n+0000ab00: 746f 7220 7072 6f64 7563 742e 0a20 2020 tor product.. \n+0000ab10: 2020 2020 2020 2020 20e2 8098 2ee2 8099 .......\n+0000ab20: 0a76 6563 746f 7220 2020 2020 20e2 8098 .vector ...\n+0000ab30: 2ae2 8099 206f 7220 2020 7363 616c 6172 *... or scalar\n+0000ab40: 2020 2020 2020 2220 2020 2020 2020 2020 \" \n+0000ab50: 2020 220a 2020 2020 2020 2020 2020 2020 \". \n+0000ab60: e280 982e e280 990a 7665 6374 6f72 2020 ........vector \n+0000ab70: 2020 2020 e280 982a e280 9920 2020 2020 ...*... \n+0000ab80: 2076 6563 746f 7220 2020 2020 2076 6563 vector vec\n+0000ab90: 746f 7220 2020 2020 2056 6563 746f 7220 tor Vector \n+0000aba0: 6372 6f73 732d 7072 6f64 7563 742e 0a76 cross-product..v\n+0000abb0: 6563 746f 7220 2020 2020 20e2 8098 2ee2 ector .....\n+0000abc0: 8099 2020 2020 2020 7665 6374 6f72 2020 .. vector \n+0000abd0: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n+0000abe0: 5665 6374 6f72 2064 6f74 2070 726f 6475 Vector dot produ\n+0000abf0: 6374 2e0a 7363 616c 6172 2020 2020 2020 ct..scalar \n+0000ac00: e280 985e e280 9920 2020 2020 2073 6361 ...^... sca\n+0000ac10: 6c61 7220 2020 2020 2073 6361 6c61 7220 lar scalar \n+0000ac20: 2020 2020 2052 6169 7365 2073 6361 6c61 Raise scala\n+0000ac30: 7220 746f 2073 6361 6c61 7220 706f 7765 r to scalar powe\n+0000ac40: 722e 0a74 7261 6e73 666f 726d 2020 20e2 r..transform .\n+0000ac50: 8098 5ee2 8099 2020 2020 2020 696e 7465 ..^... inte\n+0000ac60: 6765 7220 2020 2020 7472 616e 7366 6f72 ger transfor\n+0000ac70: 6d20 2020 5261 6973 6520 7472 616e 7366 m Raise transf\n+0000ac80: 6f72 6d20 746f 2069 6e74 6567 6572 2070 orm to integer p\n+0000ac90: 6f77 6572 2e0a 7472 616e 7366 6f72 6d20 ower..transform \n+0000aca0: 2020 e280 982a e280 9920 6f72 2020 2070 ...*... or p\n+0000acb0: 6f69 6e74 2020 2020 2020 2070 6f69 6e74 oint point\n+0000acc0: 2020 2020 2020 2041 6666 696e 6520 706f Affine po\n+0000acd0: 696e 7420 7472 616e 7366 6f72 6d20 2872 int transform (r\n+0000ace0: 6967 6874 2d74 6f2d 6c65 6674 292e 0a20 ight-to-left).. \n+0000acf0: 2020 2020 2020 2020 2020 20e2 8098 2ee2 .....\n+0000ad00: 8099 0a74 7261 6e73 666f 726d 2020 20e2 ...transform .\n+0000ad10: 8098 2ae2 8099 206f 7220 2020 7665 6374 ..*... or vect\n+0000ad20: 6f72 2020 2020 2020 7665 6374 6f72 2020 or vector \n+0000ad30: 2020 2020 4166 6669 6e65 2076 6563 746f Affine vecto\n+0000ad40: 7220 7472 616e 7366 6f72 6d20 2872 6967 r transform (rig\n+0000ad50: 6874 2d74 6f2d 6c65 6674 292e 0a20 2020 ht-to-left).. \n+0000ad60: 2020 2020 2020 2020 20e2 8098 2ee2 8099 .......\n+0000ad70: 0a74 7261 6e73 666f 726d 2020 20e2 8098 .transform ...\n+0000ad80: 2ae2 8099 206f 7220 2020 7472 616e 7366 *... or transf\n+0000ad90: 6f72 6d20 2020 7472 616e 7366 6f72 6d20 orm transform \n+0000ada0: 2020 5472 616e 7366 6f72 6d20 636f 6d70 Transform comp\n+0000adb0: 6f73 6974 696f 6e20 2872 6967 6874 2d74 osition (right-t\n+0000adc0: 6f2d 6c65 6674 292e 0a20 2020 2020 2020 o-left).. \n+0000add0: 2020 2020 20e2 8098 2ee2 8099 0a70 6f69 ........poi\n+0000ade0: 6e74 2020 2020 2020 20e2 8098 7468 656e nt ...then\n+0000adf0: e280 9920 2020 7472 616e 7366 6f72 6d20 ... transform \n+0000ae00: 2020 706f 696e 7420 2020 2020 2020 4166 point Af\n+0000ae10: 6669 6e65 2070 6f69 6e74 2074 7261 6e73 fine point trans\n+0000ae20: 666f 726d 2028 6c65 6674 2d74 6f2d 7269 form (left-to-ri\n+0000ae30: 6768 7429 2e0a 7665 6374 6f72 2020 2020 ght)..vector \n+0000ae40: 2020 e280 9874 6865 6ee2 8099 2020 2074 ...then... t\n+0000ae50: 7261 6e73 666f 726d 2020 2076 6563 746f ransform vecto\n+0000ae60: 7220 2020 2020 2041 6666 696e 6520 7665 r Affine ve\n+0000ae70: 6374 6f72 2074 7261 6e73 666f 726d 2028 ctor transform (\n+0000ae80: 6c65 6674 2d74 6f2d 7269 6768 7429 2e0a left-to-right)..\n+0000ae90: 7472 616e 7366 6f72 6d20 2020 e280 9874 transform ...t\n+0000aea0: 6865 6ee2 8099 2020 2074 7261 6e73 666f hen... transfo\n+0000aeb0: 726d 2020 2074 7261 6e73 666f 726d 2020 rm transform \n+0000aec0: 2054 7261 6e73 666f 726d 2063 6f6d 706f Transform compo\n+0000aed0: 7369 7469 6f6e 2028 6c65 6674 2d74 6f2d sition (left-to-\n+0000aee0: 7269 6768 7429 2e0a 7363 616c 6172 2020 right)..scalar \n+0000aef0: 2020 2020 e280 982f e280 9920 2020 2020 .../... \n+0000af00: 2073 6361 6c61 7220 2020 2020 2073 6361 scalar sca\n+0000af10: 6c61 7220 2020 2020 2053 6361 6c61 7220 lar Scalar \n+0000af20: 6469 7669 7369 6f6e 2e0a 7665 6374 6f72 division..vector\n+0000af30: 2020 2020 2020 e280 982f e280 9920 2020 .../... \n+0000af40: 2020 2073 6361 6c61 7220 2020 2020 2076 scalar v\n+0000af50: 6563 746f 7220 2020 2020 2056 6563 746f ector Vecto\n+0000af60: 7220 636f 6d70 6f6e 656e 742d 7769 7365 r component-wise\n+0000af70: 2064 6976 6973 696f 6e20 6279 2073 6361 division by sca\n+0000af80: 6c61 722e 0a70 6f69 6e74 2020 2020 2020 lar..point \n+0000af90: 20e2 8098 27e2 8099 2020 2020 2020 e280 ...'... ..\n+0000afa0: 9878 e280 992c 20e2 8098 79e2 8099 2c20 .x..., ...y..., \n+0000afb0: 2020 7363 616c 6172 2020 2020 2020 506f scalar Po\n+0000afc0: 696e 7420 636f 6d70 6f6e 656e 7420 6578 int component ex\n+0000afd0: 7472 6163 7469 6f6e 2e0a 2020 2020 2020 traction.. \n+0000afe0: 2020 2020 2020 2020 2020 2020 2020 206f o\n+0000aff0: 7220 e280 987a e280 990a 7665 6374 6f72 r ...z....vector\n+0000b000: 2020 2020 2020 e280 9827 e280 9920 2020 ...'... \n+0000b010: 2020 20e2 8098 78e2 8099 2c20 e280 9879 ...x..., ...y\n+0000b020: e280 992c 2020 2073 6361 6c61 7220 2020 ..., scalar \n+0000b030: 2020 2056 6563 746f 7220 636f 6d70 6f6e Vector compon\n+0000b040: 656e 7420 6578 7472 6163 7469 6f6e 2e0a ent extraction..\n+0000b050: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0000b060: 2020 2020 206f 7220 e280 987a e280 990a or ...z....\n+0000b070: 0a4f 7065 7261 746f 7220 7072 6563 6564 .Operator preced\n+0000b080: 656e 6365 2069 7320 7368 6f77 6e20 696e ence is shown in\n+0000b090: 2074 6869 7320 7461 626c 652e 0a4f 7020 this table..Op \n+0000b0a0: 2020 2020 2020 5072 6563 6564 656e 6365 Precedence\n+0000b0b0: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n 0000b0c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000b0d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a e280 -------------...\n-0000b0e0: 9827 e280 9920 2020 2020 2068 6967 6865 .'... highe\n-0000b0f0: 7374 2028 6d6f 7374 2074 6967 6874 6c79 st (most tightly\n-0000b100: 2062 696e 6469 6e67 290a e280 985e e280 binding)....^..\n-0000b110: 990a e280 982d e280 9920 2020 2020 2028 .....-... (\n-0000b120: 756e 6172 7920 6e65 6761 7469 6f6e 290a unary negation).\n-0000b130: e280 982a e280 990a e280 982e e280 990a ...*............\n-0000b140: e280 982f e280 990a e280 982b e280 990a .../.......+....\n-0000b150: e280 982d e280 990a e280 9874 6865 6ee2 ...-.......then.\n-0000b160: 8099 2020 206c 6f77 6573 7420 286c 6561 .. lowest (lea\n-0000b170: 7374 2074 6967 6874 6c79 2062 696e 6469 st tightly bindi\n-0000b180: 6e67 290a 0a41 6c6c 206f 7065 7261 7469 ng)..All operati\n-0000b190: 6f6e 7320 6172 6520 6c65 6674 2d61 7373 ons are left-ass\n-0000b1a0: 6f63 6961 7469 7665 2065 7863 6570 7420 ociative except \n-0000b1b0: 666f 7220 e280 985e e280 992e 2020 5061 for ...^.... Pa\n-0000b1c0: 7265 6e74 6865 7365 7320 e280 9828 2029 rentheses ...( )\n-0000b1d0: e280 990a 6172 6520 7573 6564 2066 6f72 ....are used for\n-0000b1e0: 2067 726f 7570 696e 6720 746f 206f 7665 grouping to ove\n-0000b1f0: 7272 6964 6520 7072 6563 6564 656e 6365 rride precedence\n-0000b200: 2069 6e20 7468 6520 7573 7561 6c20 7761 in the usual wa\n-0000b210: 792e 0a0a 2020 2041 7320 796f 7520 6361 y... As you ca\n-0000b220: 6e20 7365 652c 2074 6865 2064 6f74 206f n see, the dot o\n-0000b230: 7065 7261 746f 7220 e280 982e e280 9920 perator ....... \n-0000b240: 6973 2075 7375 616c 6c79 2061 2073 796e is usually a syn\n-0000b250: 6f6e 796d 2066 6f72 0a72 756e 2d6f 662d onym for.run-of-\n-0000b260: 7468 652d 6d69 6c6c 206d 756c 7469 706c the-mill multipl\n-0000b270: 6963 6174 696f 6e2c 20e2 8098 2ae2 8099 ication, ...*...\n-0000b280: 2e20 2054 6865 206d 6561 6e69 6e67 7320 . 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(1,2,3) \n-0000b370: 7468 656e 2073 6361 6c65 2832 2920 7468 then scale(2) th\n-0000b380: 656e 2072 6f74 6174 6528 3330 2920 7468 en rotate(30) th\n-0000b390: 656e 2074 7261 6e73 6c61 7465 285b 312c en translate([1,\n-0000b3a0: 332c 305d 290a 6578 7072 6573 7365 7320 3,0]).expresses \n-0000b3b0: 6120 7365 7269 6573 206f 6620 7375 6363 a series of succ\n-0000b3c0: 6573 7369 7665 206d 6f64 6966 6963 6174 essive modificat\n-0000b3d0: 696f 6e73 2074 6f20 7468 6520 706f 696e ions to the poin\n-0000b3e0: 742c 2077 6865 7265 6173 2074 6865 0a65 t, whereas the.e\n-0000b3f0: 7175 6976 616c 656e 7420 666f 726d 0a20 quivalent form. \n-0000b400: 2020 2020 7472 616e 736c 6174 6528 5b31 translate([1\n-0000b410: 2c33 2c30 5d29 202a 2072 6f74 6174 6528 ,3,0]) * rotate(\n-0000b420: 3330 2920 2a20 7363 616c 6528 3229 202a 30) * scale(2) *\n-0000b430: 2028 312c 322c 3329 0a77 696c 6c20 6265 (1,2,3).will be\n-0000b440: 2069 6e74 7569 7469 7665 206f 6e6c 7920 intuitive only \n-0000b450: 746f 206d 6174 6865 6d61 7469 6369 616e to mathematician\n-0000b460: 7320 2861 6e64 2070 6572 6861 7073 2041 s (and perhaps A\n-0000b470: 7261 6269 6320 6c61 6e67 7561 6765 0a72 rabic language.r\n-0000b480: 6561 6465 7273 292e 0a0a 1f0a 4669 6c65 eaders).....File\n-0000b490: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-0000b4a0: 4e6f 6465 3a20 556e 6172 7920 666f 726d Node: Unary form\n-0000b4b0: 732c 2020 5072 6576 3a20 5477 6f2d 6f70 s, Prev: Two-op\n-0000b4c0: 6572 616e 6420 2862 696e 6172 7929 2066 erand (binary) f\n-0000b4d0: 6f72 6d73 2c20 2055 703a 2041 7269 7468 orms, Up: Arith\n-0000b4e0: 6d65 7469 630a 0a33 2e31 2e34 2e32 2055 metic..3.1.4.2 U\n-0000b4f0: 6e61 7279 2066 6f72 6d73 0a2e 2e2e 2e2e nary forms......\n-0000b500: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a ................\n-0000b510: 556e 6172 7920 6f72 206f 6e65 2d6f 7065 Unary or one-ope\n-0000b520: 7261 6e64 2066 6f72 6d73 2061 7265 2073 rand forms are s\n-0000b530: 756d 6d61 7269 7a65 6420 696e 2074 6865 ummarized in the\n-0000b540: 2066 6f6c 6c6f 7769 6e67 2074 6162 6c65 following table\n-0000b550: 2c20 7768 6572 650a e280 9858 e280 9920 , where....X... \n-0000b560: 7374 616e 6473 2066 6f72 2074 6865 206f stands for the o\n-0000b570: 7065 7261 6e64 2e0a 4f70 2020 2020 2020 perand..Op \n-0000b580: 2020 2020 2020 204f 7065 7261 6e64 2020 Operand \n-0000b590: 2020 2052 6573 756c 7420 2020 2020 2044 Result D\n-0000b5a0: 6573 6372 6970 7469 6f6e 0a2d 2d2d 2d2d escription.-----\n+0000b0d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a e280 9827 -----------....'\n+0000b0e0: e280 9920 2020 2020 2068 6967 6865 7374 ... highest\n+0000b0f0: 2028 6d6f 7374 2074 6967 6874 6c79 2062 (most tightly b\n+0000b100: 696e 6469 6e67 290a e280 985e e280 990a inding)....^....\n+0000b110: e280 982d e280 9920 2020 2020 2028 756e ...-... (un\n+0000b120: 6172 7920 6e65 6761 7469 6f6e 290a e280 ary negation)...\n+0000b130: 982a e280 990a e280 982e e280 990a e280 .*..............\n+0000b140: 982f e280 990a e280 982b e280 990a e280 ./.......+......\n+0000b150: 982d e280 990a e280 9874 6865 6ee2 8099 .-.......then...\n+0000b160: 2020 206c 6f77 6573 7420 286c 6561 7374 lowest (least\n+0000b170: 2074 6967 6874 6c79 2062 696e 6469 6e67 tightly binding\n+0000b180: 290a 0a41 6c6c 206f 7065 7261 7469 6f6e )..All operation\n+0000b190: 7320 6172 6520 6c65 6674 2d61 7373 6f63 s are left-assoc\n+0000b1a0: 6961 7469 7665 2065 7863 6570 7420 666f iative except fo\n+0000b1b0: 7220 e280 985e e280 992e 2020 5061 7265 r ...^.... Pare\n+0000b1c0: 6e74 6865 7365 7320 e280 9828 2029 e280 ntheses ...( )..\n+0000b1d0: 990a 6172 6520 7573 6564 2066 6f72 2067 ..are used for g\n+0000b1e0: 726f 7570 696e 6720 746f 206f 7665 7272 rouping to overr\n+0000b1f0: 6964 6520 7072 6563 6564 656e 6365 2069 ide precedence i\n+0000b200: 6e20 7468 6520 7573 7561 6c20 7761 792e n the usual way.\n+0000b210: 0a0a 2020 2041 7320 796f 7520 6361 6e20 .. As you can \n+0000b220: 7365 652c 2074 6865 2064 6f74 206f 7065 see, the dot ope\n+0000b230: 7261 746f 7220 e280 982e e280 9920 6973 rator ....... is\n+0000b240: 2075 7375 616c 6c79 2061 2073 796e 6f6e usually a synon\n+0000b250: 796d 2066 6f72 0a72 756e 2d6f 662d 7468 ym for.run-of-th\n+0000b260: 652d 6d69 6c6c 206d 756c 7469 706c 6963 e-mill multiplic\n+0000b270: 6174 696f 6e2c 20e2 8098 2ae2 8099 2e20 ation, ...*.... \n+0000b280: 2054 6865 206d 6561 6e69 6e67 7320 6469 The meanings di\n+0000b290: 6666 6572 206f 6e6c 7920 666f 720a 7665 ffer only for.ve\n+0000b2a0: 6374 6f72 206f 7065 7261 6e64 732e 2020 ctor operands. \n+0000b2b0: 5468 6520 e280 9874 6865 6ee2 8099 206f The ...then... o\n+0000b2c0: 7065 7261 746f 7220 6d65 7265 6c79 2072 perator merely r\n+0000b2d0: 6576 6572 7365 7320 7468 6520 6f70 6572 everses the oper\n+0000b2e0: 616e 6420 6f72 6465 720a 7769 7468 2072 and order.with r\n+0000b2f0: 6573 7065 6374 2074 6f20 6e6f 726d 616c espect to normal\n+0000b300: 206d 756c 7469 706c 6963 6174 696f 6e20 multiplication \n+0000b310: e280 982a e280 992e 2020 5468 6520 696e ...*.... 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(1,2,3) th\n+0000b370: 656e 2073 6361 6c65 2832 2920 7468 656e en scale(2) then\n+0000b380: 2072 6f74 6174 6528 3330 2920 7468 656e rotate(30) then\n+0000b390: 2074 7261 6e73 6c61 7465 285b 312c 332c translate([1,3,\n+0000b3a0: 305d 290a 6578 7072 6573 7365 7320 6120 0]).expresses a \n+0000b3b0: 7365 7269 6573 206f 6620 7375 6363 6573 series of succes\n+0000b3c0: 7369 7665 206d 6f64 6966 6963 6174 696f sive modificatio\n+0000b3d0: 6e73 2074 6f20 7468 6520 706f 696e 742c ns to the point,\n+0000b3e0: 2077 6865 7265 6173 2074 6865 0a65 7175 whereas the.equ\n+0000b3f0: 6976 616c 656e 7420 666f 726d 0a20 2020 ivalent form. \n+0000b400: 2020 7472 616e 736c 6174 6528 5b31 2c33 translate([1,3\n+0000b410: 2c30 5d29 202a 2072 6f74 6174 6528 3330 ,0]) * rotate(30\n+0000b420: 2920 2a20 7363 616c 6528 3229 202a 2028 ) * scale(2) * (\n+0000b430: 312c 322c 3329 0a77 696c 6c20 6265 2069 1,2,3).will be i\n+0000b440: 6e74 7569 7469 7665 206f 6e6c 7920 746f ntuitive only to\n+0000b450: 206d 6174 6865 6d61 7469 6369 616e 7320 mathematicians \n+0000b460: 2861 6e64 2070 6572 6861 7073 2041 7261 (and perhaps Ara\n+0000b470: 6269 6320 6c61 6e67 7561 6765 0a72 6561 bic language.rea\n+0000b480: 6465 7273 292e 0a0a 1f0a 4669 6c65 3a20 ders).....File: \n+0000b490: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+0000b4a0: 6465 3a20 556e 6172 7920 666f 726d 732c de: Unary forms,\n+0000b4b0: 2020 5072 6576 3a20 5477 6f2d 6f70 6572 Prev: Two-oper\n+0000b4c0: 616e 6420 2862 696e 6172 7929 2066 6f72 and (binary) for\n+0000b4d0: 6d73 2c20 2055 703a 2041 7269 7468 6d65 ms, Up: Arithme\n+0000b4e0: 7469 630a 0a33 2e31 2e34 2e32 2055 6e61 tic..3.1.4.2 Una\n+0000b4f0: 7279 2066 6f72 6d73 0a2e 2e2e 2e2e 2e2e ry forms........\n+0000b500: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 556e ..............Un\n+0000b510: 6172 7920 6f72 206f 6e65 2d6f 7065 7261 ary or one-opera\n+0000b520: 6e64 2066 6f72 6d73 2061 7265 2073 756d nd forms are sum\n+0000b530: 6d61 7269 7a65 6420 696e 2074 6865 2066 marized in the f\n+0000b540: 6f6c 6c6f 7769 6e67 2074 6162 6c65 2c20 ollowing table, \n+0000b550: 7768 6572 650a e280 9858 e280 9920 7374 where....X... st\n+0000b560: 616e 6473 2066 6f72 2074 6865 206f 7065 ands for the ope\n+0000b570: 7261 6e64 2e0a 4f70 2020 2020 2020 2020 rand..Op \n+0000b580: 2020 2020 204f 7065 7261 6e64 2020 2020 Operand \n+0000b590: 2052 6573 756c 7420 2020 2020 2044 6573 Result Des\n+0000b5a0: 6372 6970 7469 6f6e 0a2d 2d2d 2d2d 2d2d cription.-------\n 0000b5b0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 0000b5e0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-0000b5f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ---------------.\n-0000b600: e280 982d 58e2 8099 2020 2020 2020 2020 ...-X... \n-0000b610: 2020 2073 6361 6c61 7220 2020 2020 2073 scalar s\n-0000b620: 6361 6c61 7220 2020 2020 2055 6e61 7279 calar Unary\n-0000b630: 2073 6361 6c61 7220 6e65 6761 7469 6f6e scalar negation\n-0000b640: 2e0a e280 982d 58e2 8099 2020 2020 2020 .....-X... \n-0000b650: 2020 2020 2076 6563 746f 7220 2020 2020 vector \n-0000b660: 2076 6563 746f 7220 2020 2020 2055 6e61 vector Una\n-0000b670: 7279 2076 6563 746f 7220 6e65 6761 7469 ry vector negati\n-0000b680: 6f6e 2e0a e280 987c 587c e280 9920 2020 on.....|X|... \n-0000b690: 2020 2020 2020 2076 6563 746f 7220 2020 vector \n-0000b6a0: 2020 2073 6361 6c61 7220 2020 2020 2056 scalar V\n-0000b6b0: 6563 746f 7220 6c65 6e67 7468 2e0a e280 ector length....\n-0000b6c0: 9875 6e69 7428 5829 e280 9920 2020 2020 .unit(X)... \n-0000b6d0: 2076 6563 746f 7220 2020 2020 2076 6563 vector vec\n-0000b6e0: 746f 7220 2020 2020 2055 6e69 7420 7665 tor Unit ve\n-0000b6f0: 6374 6f72 2077 6974 6820 7361 6d65 2064 ctor with same d\n-0000b700: 6972 6563 7469 6f6e 2e0a e280 9873 7172 irection.....sqr\n-0000b710: 7428 5829 e280 9920 2020 2020 2073 6361 t(X)... sca\n-0000b720: 6c61 7220 2020 2020 2073 6361 6c61 7220 lar scalar \n-0000b730: 2020 2020 2053 6361 6c61 7220 7371 7561 Scalar squa\n-0000b740: 7265 2072 6f6f 742e 0ae2 8098 7369 6e28 re root.....sin(\n-0000b750: 5829 e280 9920 2020 2020 2020 7363 616c X)... scal\n-0000b760: 6172 2020 2020 2020 7363 616c 6172 2020 ar scalar \n-0000b770: 2020 2020 5472 6967 6f6e 6f6d 6574 7269 Trigonometri\n-0000b780: 6320 7369 6e65 2028 e280 9858 e280 9920 c sine (...X... \n-0000b790: 696e 2064 6567 7265 6573 292e 0ae2 8098 in degrees).....\n-0000b7a0: 636f 7328 5829 e280 9920 2020 2020 2020 cos(X)... \n-0000b7b0: 7363 616c 6172 2020 2020 2020 7363 616c scalar scal\n-0000b7c0: 6172 2020 2020 2020 5472 6967 6f6e 6f6d ar Trigonom\n-0000b7d0: 6574 7269 6320 636f 7369 6e65 2028 e280 etric cosine (..\n-0000b7e0: 9858 e280 9920 696e 2064 6567 7265 6573 .X... in degrees\n-0000b7f0: 292e 0ae2 8098 6173 696e 2858 29e2 8099 ).....asin(X)...\n-0000b800: 2020 2020 2020 7363 616c 6172 2020 2020 scalar \n-0000b810: 2020 7363 616c 6172 2020 2020 2020 496e scalar In\n-0000b820: 7665 7273 6520 7369 6e65 2028 e280 9858 verse sine (...X\n-0000b830: e280 9920 696e 2064 6567 7265 6573 292e ... in degrees).\n-0000b840: 0ae2 8098 6163 6f73 2858 29e2 8099 2020 ....acos(X)... \n-0000b850: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n-0000b860: 7363 616c 6172 2020 2020 2020 496e 7665 scalar Inve\n-0000b870: 7273 6520 636f 7369 6e65 2028 e280 9858 rse cosine (...X\n-0000b880: e280 9920 696e 2064 6567 7265 6573 292e ... in degrees).\n-0000b890: 0ae2 8098 6174 616e 3228 582c 5929 e280 ....atan2(X,Y)..\n-0000b8a0: 9920 2020 7363 616c 6172 2020 2020 2020 . scalar \n-0000b8b0: 7363 616c 6172 2020 2020 2020 506f 6c61 scalar Pola\n-0000b8c0: 7220 616e 676c 6520 696e 2064 6567 7265 r angle in degre\n-0000b8d0: 6573 206f 6620 7665 6374 6f72 205b 582c es of vector [X,\n-0000b8e0: 595d 2e0a e280 9869 6e76 6572 7365 2858 Y].....inverse(X\n-0000b8f0: 29e2 8099 2020 2074 7261 6e73 666f 726d )... transform\n-0000b900: 2020 2074 7261 6e73 666f 726d 2020 2049 transform I\n-0000b910: 6e76 6572 7365 2074 7261 6e73 666f 726d nverse transform\n-0000b920: 2e0a 0a45 7272 6f72 7320 6172 6520 7265 ...Errors are re\n-0000b930: 706f 7274 6564 2077 6865 6e20 e280 987c ported when ...|\n-0000b940: 587c e280 992c 20e2 8098 756e 6974 e280 X|..., ...unit..\n-0000b950: 992c 20e2 8098 6173 696e e280 992c 20e2 ., ...asin..., .\n-0000b960: 8098 6163 6f73 e280 992c 20e2 8098 7371 ..acos..., ...sq\n-0000b970: 7274 e280 992c 20e2 8098 6174 616e 32e2 rt..., ...atan2.\n-0000b980: 8099 2c0a 616e 6420 e280 9869 6e76 6572 ..,.and ...inver\n-0000b990: 7365 e280 9920 6661 696c 2064 7565 2074 se... fail due t\n-0000b9a0: 6f20 6f70 6572 616e 6473 206f 7574 7369 o operands outsi\n-0000b9b0: 6465 2074 6865 6972 2072 6573 7065 6374 de their respect\n-0000b9c0: 6976 6520 646f 6d61 696e 732e 0a0a 1f0a ive domains.....\n-0000b9d0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n-0000b9e0: 6f2c 2020 4e6f 6465 3a20 4f70 7469 6f6e o, Node: 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As.shown \n-0000bab0: 6162 6f76 652c 2074 6865 7920 6172 6520 above, they are \n-0000bac0: 6769 7665 6e20 6173 2063 6f6d 6d61 2d73 given as comma-s\n-0000bad0: 6570 6172 6174 6564 206b 6579 2d76 616c eparated key-val\n-0000bae0: 7565 2070 6169 7273 2e0a 0a2a 204d 656e ue pairs...* Men\n-0000baf0: 753a 0a0a 2a20 5053 5472 6963 6b73 206f u:..* PSTricks o\n-0000bb00: 7074 696f 6e73 3a3a 2020 2020 2020 2020 ptions:: \n-0000bb10: 2020 2020 4f70 7469 6f6e 7320 696e 6865 Options inhe\n-0000bb20: 7269 7465 6420 6672 6f6d 20e2 8098 5053 rited from ...PS\n-0000bb30: 5472 6963 6b73 e280 992e 0a2a 2054 696b Tricks.....* Tik\n-0000bb40: 5a2f 5047 4620 6f70 7469 6f6e 733a 3a20 Z/PGF options:: \n-0000bb50: 2020 2020 2020 2020 2020 204f 7074 696f Optio\n-0000bb60: 6e73 2069 6e68 6572 6974 6564 2066 726f ns inherited fro\n-0000bb70: 6d20 e280 9854 696b 5a2f 5047 46e2 8099 m ...TikZ/PGF...\n-0000bb80: 2e0a 2a20 446f 7473 2069 6e20 5469 6b5a ..* Dots in TikZ\n-0000bb90: 2f50 4746 3a3a 2020 2020 2020 2020 2020 /PGF:: \n-0000bba0: 2020 536b 6574 6368 2075 7365 7320 e280 Sketch uses ..\n-0000bbb0: 9854 696b 5a2f 5047 46e2 8099 2063 6972 .TikZ/PGF... cir\n-0000bbc0: 636c 6573 2066 6f72 2064 6f74 732e 0a2a cles for dots..*\n-0000bbd0: 2054 696b 5a2f 5047 4620 7573 6572 2d64 TikZ/PGF user-d\n-0000bbe0: 6566 696e 6564 2073 7479 6c65 733a 3a20 efined styles:: \n-0000bbf0: 2053 7570 706f 7274 2066 6f72 20e2 8098 Support for ...\n-0000bc00: 5469 6b5a 2f50 4746 e280 9920 6e61 6d65 TikZ/PGF... name\n-0000bc10: 642c 2075 7365 722d 6465 6669 6e65 6420 d, user-defined \n-0000bc20: 7374 796c 6573 2e0a 2a20 5472 616e 7370 styles..* Transp\n-0000bc30: 6172 656e 6379 3a3a 2020 2020 2020 2020 arency:: \n-0000bc40: 2020 2020 2020 2020 5365 652d 7468 726f See-thro\n-0000bc50: 7567 6820 706f 6c79 676f 6e73 2e0a 2a20 ugh polygons..* \n-0000bc60: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n-0000bc70: 3a3a 2020 2020 2020 2020 2020 2020 4f70 :: Op\n-0000bc80: 7469 6f6e 7320 7573 6564 2062 7920 e280 tions used by ..\n-0000bc90: 9873 6b65 7463 68e2 8099 2e0a 0a1f 0a46 .sketch........F\n-0000bca0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-0000bcb0: 2c20 204e 6f64 653a 2050 5354 7269 636b , Node: PSTrick\n-0000bcc0: 7320 6f70 7469 6f6e 732c 2020 4e65 7874 s options, Next\n-0000bcd0: 3a20 5469 6b5a 2f50 4746 206f 7074 696f : TikZ/PGF optio\n-0000bce0: 6e73 2c20 2050 7265 763a 204f 7074 696f ns, Prev: Optio\n-0000bcf0: 6e73 2c20 2055 703a 204f 7074 696f 6e73 ns, Up: Options\n-0000bd00: 0a0a 332e 312e 352e 3120 e280 9850 5354 ..3.1.5.1 ...PST\n-0000bd10: 7269 636b 73e2 8099 206f 7074 696f 6e73 ricks... options\n-0000bd20: 0a2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000bd30: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a57 6865 .............Whe\n-0000bd40: 6e20 e280 986c 616e 6775 6167 6520 7073 n ...language ps\n-0000bd50: 7472 6963 6b73 e280 9920 6973 2073 656c tricks... is sel\n-0000bd60: 6563 7465 6420 2874 6865 2064 6566 6175 ected (the defau\n-0000bd70: 6c74 292c 2070 6572 6d69 7373 6962 6c65 lt), permissible\n-0000bd80: 0a6b 6579 2d76 616c 7565 2070 6169 7273 .key-value pairs\n-0000bd90: 2069 6e63 6c75 6465 2061 6c6c 2074 686f include all tho\n-0000bda0: 7365 2066 6f72 2073 696d 696c 6172 20e2 se for similar .\n-0000bdb0: 8098 5053 5472 6963 6b73 e280 9920 6f62 ..PSTricks... ob\n-0000bdc0: 6a65 6374 732e 2020 466f 720a 6578 616d jects. 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sketch\n-0000c7d0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 446f .info, Node: Do\n-0000c7e0: 7473 2069 6e20 5469 6b5a 2f50 4746 2c20 ts in TikZ/PGF, \n-0000c7f0: 204e 6578 743a 2054 696b 5a2f 5047 4620 Next: TikZ/PGF \n-0000c800: 7573 6572 2d64 6566 696e 6564 2073 7479 user-defined sty\n-0000c810: 6c65 732c 2020 5072 6576 3a20 5469 6b5a les, Prev: TikZ\n-0000c820: 2f50 4746 206f 7074 696f 6e73 2c20 2055 /PGF options, U\n-0000c830: 703a 204f 7074 696f 6e73 0a0a 332e 312e p: Options..3.1.\n-0000c840: 352e 3320 446f 7473 2069 6e20 e280 9854 5.3 Dots in ...T\n-0000c850: 696b 5a2f 5047 46e2 8099 0a2e 2e2e 2e2e ikZ/PGF.........\n+0000b5f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a e280 -------------...\n+0000b600: 982d 58e2 8099 2020 2020 2020 2020 2020 .-X... \n+0000b610: 2073 6361 6c61 7220 2020 2020 2073 6361 scalar sca\n+0000b620: 6c61 7220 2020 2020 2055 6e61 7279 2073 lar Unary s\n+0000b630: 6361 6c61 7220 6e65 6761 7469 6f6e 2e0a calar negation..\n+0000b640: e280 982d 58e2 8099 2020 2020 2020 2020 ...-X... \n+0000b650: 2020 2076 6563 746f 7220 2020 2020 2076 vector v\n+0000b660: 6563 746f 7220 2020 2020 2055 6e61 7279 ector Unary\n+0000b670: 2076 6563 746f 7220 6e65 6761 7469 6f6e vector negation\n+0000b680: 2e0a e280 987c 587c e280 9920 2020 2020 .....|X|... \n+0000b690: 2020 2020 2076 6563 746f 7220 2020 2020 vector \n+0000b6a0: 2073 6361 6c61 7220 2020 2020 2056 6563 scalar Vec\n+0000b6b0: 746f 7220 6c65 6e67 7468 2e0a e280 9875 tor length.....u\n+0000b6c0: 6e69 7428 5829 e280 9920 2020 2020 2076 nit(X)... v\n+0000b6d0: 6563 746f 7220 2020 2020 2076 6563 746f ector vecto\n+0000b6e0: 7220 2020 2020 2055 6e69 7420 7665 6374 r Unit vect\n+0000b6f0: 6f72 2077 6974 6820 7361 6d65 2064 6972 or with same dir\n+0000b700: 6563 7469 6f6e 2e0a e280 9873 7172 7428 ection.....sqrt(\n+0000b710: 5829 e280 9920 2020 2020 2073 6361 6c61 X)... scala\n+0000b720: 7220 2020 2020 2073 6361 6c61 7220 2020 r scalar \n+0000b730: 2020 2053 6361 6c61 7220 7371 7561 7265 Scalar square\n+0000b740: 2072 6f6f 742e 0ae2 8098 7369 6e28 5829 root.....sin(X)\n+0000b750: e280 9920 2020 2020 2020 7363 616c 6172 ... scalar\n+0000b760: 2020 2020 2020 7363 616c 6172 2020 2020 scalar \n+0000b770: 2020 5472 6967 6f6e 6f6d 6574 7269 6320 Trigonometric \n+0000b780: 7369 6e65 2028 e280 9858 e280 9920 696e sine (...X... in\n+0000b790: 2064 6567 7265 6573 292e 0ae2 8098 636f degrees).....co\n+0000b7a0: 7328 5829 e280 9920 2020 2020 2020 7363 s(X)... sc\n+0000b7b0: 616c 6172 2020 2020 2020 7363 616c 6172 alar scalar\n+0000b7c0: 2020 2020 2020 5472 6967 6f6e 6f6d 6574 Trigonomet\n+0000b7d0: 7269 6320 636f 7369 6e65 2028 e280 9858 ric cosine (...X\n+0000b7e0: e280 9920 696e 2064 6567 7265 6573 292e ... in degrees).\n+0000b7f0: 0ae2 8098 6173 696e 2858 29e2 8099 2020 ....asin(X)... \n+0000b800: 2020 2020 7363 616c 6172 2020 2020 2020 scalar \n+0000b810: 7363 616c 6172 2020 2020 2020 496e 7665 scalar Inve\n+0000b820: 7273 6520 7369 6e65 2028 e280 9858 e280 rse sine (...X..\n+0000b830: 9920 696e 2064 6567 7265 6573 292e 0ae2 . in degrees)...\n+0000b840: 8098 6163 6f73 2858 29e2 8099 2020 2020 ..acos(X)... \n+0000b850: 2020 7363 616c 6172 2020 2020 2020 7363 scalar sc\n+0000b860: 616c 6172 2020 2020 2020 496e 7665 7273 alar Invers\n+0000b870: 6520 636f 7369 6e65 2028 e280 9858 e280 e cosine (...X..\n+0000b880: 9920 696e 2064 6567 7265 6573 292e 0ae2 . in degrees)...\n+0000b890: 8098 6174 616e 3228 582c 5929 e280 9920 ..atan2(X,Y)... \n+0000b8a0: 2020 7363 616c 6172 2020 2020 2020 7363 scalar sc\n+0000b8b0: 616c 6172 2020 2020 2020 506f 6c61 7220 alar Polar \n+0000b8c0: 616e 676c 6520 696e 2064 6567 7265 6573 angle in degrees\n+0000b8d0: 206f 6620 7665 6374 6f72 205b 582c 595d of vector [X,Y]\n+0000b8e0: 2e0a e280 9869 6e76 6572 7365 2858 29e2 .....inverse(X).\n+0000b8f0: 8099 2020 2074 7261 6e73 666f 726d 2020 .. transform \n+0000b900: 2074 7261 6e73 666f 726d 2020 2049 6e76 transform Inv\n+0000b910: 6572 7365 2074 7261 6e73 666f 726d 2e0a erse transform..\n+0000b920: 0a45 7272 6f72 7320 6172 6520 7265 706f .Errors are repo\n+0000b930: 7274 6564 2077 6865 6e20 e280 987c 587c rted when ...|X|\n+0000b940: e280 992c 20e2 8098 756e 6974 e280 992c ..., ...unit...,\n+0000b950: 20e2 8098 6173 696e e280 992c 20e2 8098 ...asin..., ...\n+0000b960: 6163 6f73 e280 992c 20e2 8098 7371 7274 acos..., ...sqrt\n+0000b970: e280 992c 20e2 8098 6174 616e 32e2 8099 ..., ...atan2...\n+0000b980: 2c0a 616e 6420 e280 9869 6e76 6572 7365 ,.and ...inverse\n+0000b990: e280 9920 6661 696c 2064 7565 2074 6f20 ... fail due to \n+0000b9a0: 6f70 6572 616e 6473 206f 7574 7369 6465 operands outside\n+0000b9b0: 2074 6865 6972 2072 6573 7065 6374 6976 their respectiv\n+0000b9c0: 6520 646f 6d61 696e 732e 0a0a 1f0a 4669 e domains.....Fi\n+0000b9d0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n+0000b9e0: 2020 4e6f 6465 3a20 4f70 7469 6f6e 732c Node: Options,\n+0000b9f0: 2020 5072 6576 3a20 4172 6974 686d 6574 Prev: Arithmet\n+0000ba00: 6963 2c20 2055 703a 204c 616e 6775 6167 ic, Up: Languag\n+0000ba10: 6520 6261 7369 6373 0a0a 332e 312e 3520 e basics..3.1.5 \n+0000ba20: 4f70 7469 6f6e 730a 2d2d 2d2d 2d2d 2d2d Options.--------\n+0000ba30: 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a -----..*Syntax:*\n+0000ba40: 0a20 2020 2020 5b4b 4559 313d 5641 4c31 . [KEY1=VAL1\n+0000ba50: 2c4b 4559 323d 5641 4c32 2c2e 2e2e 5d0a ,KEY2=VAL2,...].\n+0000ba60: 4f70 7469 6f6e 7320 6172 6520 7573 6564 Options are used\n+0000ba70: 2074 6f20 7370 6563 6966 7920 6465 7461 to specify deta\n+0000ba80: 696c 7320 6f66 2074 6865 2061 7070 6561 ils of the appea\n+0000ba90: 7261 6e63 6520 6f66 2064 7261 7761 626c rance of drawabl\n+0000baa0: 6573 2e20 2041 730a 7368 6f77 6e20 6162 es. As.shown ab\n+0000bab0: 6f76 652c 2074 6865 7920 6172 6520 6769 ove, they are gi\n+0000bac0: 7665 6e20 6173 2063 6f6d 6d61 2d73 6570 ven as comma-sep\n+0000bad0: 6172 6174 6564 206b 6579 2d76 616c 7565 arated key-value\n+0000bae0: 2070 6169 7273 2e0a 0a2a 204d 656e 753a pairs...* Menu:\n+0000baf0: 0a0a 2a20 5053 5472 6963 6b73 206f 7074 ..* PSTricks opt\n+0000bb00: 696f 6e73 3a3a 2020 2020 2020 2020 2020 ions:: \n+0000bb10: 2020 4f70 7469 6f6e 7320 696e 6865 7269 Options inheri\n+0000bb20: 7465 6420 6672 6f6d 20e2 8098 5053 5472 ted from ...PSTr\n+0000bb30: 6963 6b73 e280 992e 0a2a 2054 696b 5a2f icks.....* TikZ/\n+0000bb40: 5047 4620 6f70 7469 6f6e 733a 3a20 2020 PGF options:: \n+0000bb50: 2020 2020 2020 2020 204f 7074 696f 6e73 Options\n+0000bb60: 2069 6e68 6572 6974 6564 2066 726f 6d20 inherited from \n+0000bb70: e280 9854 696b 5a2f 5047 46e2 8099 2e0a ...TikZ/PGF.....\n+0000bb80: 2a20 446f 7473 2069 6e20 5469 6b5a 2f50 * Dots in TikZ/P\n+0000bb90: 4746 3a3a 2020 2020 2020 2020 2020 2020 GF:: \n+0000bba0: 536b 6574 6368 2075 7365 7320 e280 9854 Sketch uses ...T\n+0000bbb0: 696b 5a2f 5047 46e2 8099 2063 6972 636c ikZ/PGF... circl\n+0000bbc0: 6573 2066 6f72 2064 6f74 732e 0a2a 2054 es for dots..* T\n+0000bbd0: 696b 5a2f 5047 4620 7573 6572 2d64 6566 ikZ/PGF user-def\n+0000bbe0: 696e 6564 2073 7479 6c65 733a 3a20 2053 ined styles:: S\n+0000bbf0: 7570 706f 7274 2066 6f72 20e2 8098 5469 upport for ...Ti\n+0000bc00: 6b5a 2f50 4746 e280 9920 6e61 6d65 642c kZ/PGF... named,\n+0000bc10: 2075 7365 722d 6465 6669 6e65 6420 7374 user-defined st\n+0000bc20: 796c 6573 2e0a 2a20 5472 616e 7370 6172 yles..* Transpar\n+0000bc30: 656e 6379 3a3a 2020 2020 2020 2020 2020 ency:: \n+0000bc40: 2020 2020 2020 5365 652d 7468 726f 7567 See-throug\n+0000bc50: 6820 706f 6c79 676f 6e73 2e0a 2a20 496e h polygons..* In\n+0000bc60: 7465 726e 616c 206f 7074 696f 6e73 3a3a ternal options::\n+0000bc70: 2020 2020 2020 2020 2020 2020 4f70 7469 Opti\n+0000bc80: 6f6e 7320 7573 6564 2062 7920 e280 9873 ons used by ...s\n+0000bc90: 6b65 7463 68e2 8099 2e0a 0a1f 0a46 696c ketch........Fil\n+0000bca0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+0000bcb0: 204e 6f64 653a 2050 5354 7269 636b 7320 Node: PSTricks \n+0000bcc0: 6f70 7469 6f6e 732c 2020 4e65 7874 3a20 options, Next: \n+0000bcd0: 5469 6b5a 2f50 4746 206f 7074 696f 6e73 TikZ/PGF options\n+0000bce0: 2c20 2050 7265 763a 204f 7074 696f 6e73 , Prev: Options\n+0000bcf0: 2c20 2055 703a 204f 7074 696f 6e73 0a0a , Up: Options..\n+0000bd00: 332e 312e 352e 3120 e280 9850 5354 7269 3.1.5.1 ...PSTri\n+0000bd10: 636b 73e2 8099 206f 7074 696f 6e73 0a2e cks... options..\n+0000bd20: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+0000bd30: 2e2e 2e2e 2e2e 2e2e 2e0a 0a57 6865 6e20 ...........When \n+0000bd40: e280 986c 616e 6775 6167 6520 7073 7472 ...language pstr\n+0000bd50: 6963 6b73 e280 9920 6973 2073 656c 6563 icks... is selec\n+0000bd60: 7465 6420 2874 6865 2064 6566 6175 6c74 ted (the default\n+0000bd70: 292c 2070 6572 6d69 7373 6962 6c65 0a6b ), permissible.k\n+0000bd80: 6579 2d76 616c 7565 2070 6169 7273 2069 ey-value pairs i\n+0000bd90: 6e63 6c75 6465 2061 6c6c 2074 686f 7365 nclude all those\n+0000bda0: 2066 6f72 2073 696d 696c 6172 20e2 8098 for similar ...\n+0000bdb0: 5053 5472 6963 6b73 e280 9920 6f62 6a65 PSTricks... obje\n+0000bdc0: 6374 732e 2020 466f 720a 6578 616d 706c cts. For.exampl\n+0000bdd0: 652c 2061 2070 6f6c 7967 6f6e 206d 6967 e, a polygon mig\n+0000bde0: 6874 2068 6176 6520 7468 6520 6f70 7469 ht have the opti\n+0000bdf0: 6f6e 730a 2020 5b6c 696e 6577 6964 7468 ons. [linewidth\n+0000be00: 3d31 7074 2c6c 696e 6563 6f6c 6f72 3d62 =1pt,linecolor=b\n+0000be10: 6c75 652c 6669 6c6c 636f 6c6f 723d 6379 lue,fillcolor=cy\n+0000be20: 616e 5d0a e280 9853 6b65 7463 68e2 8099 an]....Sketch...\n+0000be30: 206d 6572 656c 7920 7061 7373 6573 2074 merely passes t\n+0000be40: 6865 7365 206f 6e20 746f 20e2 8098 5053 hese on to ...PS\n+0000be50: 5472 6963 6b73 e280 9920 7769 7468 6f75 Tricks... withou\n+0000be60: 7420 6368 6563 6b69 6e67 206f 720a 6d6f t checking or.mo\n+0000be70: 6469 6669 6361 7469 6f6e 2e20 204f 7074 dification. Opt\n+0000be80: 696f 6e20 6c69 7374 7320 6172 6520 616c ion lists are al\n+0000be90: 7761 7973 206f 7074 696f 6e61 6c2e 2020 ways optional. \n+0000bea0: 4120 6d69 7373 696e 6720 6f70 7469 6f6e A missing option\n+0000beb0: 7320 6c69 7374 0a69 7320 6571 7569 7661 s list.is equiva\n+0000bec0: 6c65 6e74 2074 6f20 616e 2065 6d70 7479 lent to an empty\n+0000bed0: 206f 6e65 20e2 8098 5b5d e280 992e 0a0a one ...[]......\n+0000bee0: 2020 2057 6865 6e20 6120 e280 9870 6f6c When a ...pol\n+0000bef0: 7967 6f6e e280 9920 6861 7320 6f70 7469 ygon... has opti\n+0000bf00: 6f6e 7320 666f 7220 626f 7468 2069 7473 ons for both its\n+0000bf10: 2066 6163 6520 616e 6420 6974 7320 6564 face and its ed\n+0000bf20: 6765 732c 2061 6e64 2074 6865 0a70 6f6c ges, and the.pol\n+0000bf30: 7967 6f6e 2069 7320 7370 6c69 7420 6279 ygon is split by\n+0000bf40: 2074 6865 2068 6964 6465 6e20 7375 7266 the hidden surf\n+0000bf50: 6163 6520 616c 676f 7269 7468 6d2c 20e2 ace algorithm, .\n+0000bf60: 8098 736b 6574 6368 e280 9920 6d75 7374 ..sketch... must\n+0000bf70: 2063 6f70 7920 7468 650a 6564 6765 206f copy the.edge o\n+0000bf80: 7074 696f 6e73 2074 6f20 e280 9870 736c ptions to ...psl\n+0000bf90: 696e 65e2 8099 7320 666f 7220 7468 6520 ine...s for the \n+0000bfa0: 6564 6765 2073 6567 6d65 6e74 7320 616e edge segments an\n+0000bfb0: 6420 7468 6520 6661 6365 206f 7074 696f d the face optio\n+0000bfc0: 6e73 2074 6f0a e280 9870 7370 6f6c 7967 ns to....pspolyg\n+0000bfd0: 6f6e e280 9973 2e20 204f 7074 696f 6e73 on...s. Options\n+0000bfe0: 206b 6e6f 776e 2074 6f20 e280 9873 6b65 known to ...ske\n+0000bff0: 7463 68e2 8099 2066 6f72 2070 7572 706f tch... for purpo\n+0000c000: 7365 7320 6f66 2074 6869 7320 7370 6c69 ses of this spli\n+0000c010: 7474 696e 670a 6f70 6572 6174 696f 6e20 tting.operation \n+0000c020: 696e 636c 7564 6520 e280 9861 7272 6f77 include ...arrow\n+0000c030: 73e2 8099 2c20 e280 9864 6173 68e2 8099 s..., ...dash...\n+0000c040: 2c20 e280 9864 6f74 7365 70e2 8099 2c20 , ...dotsep..., \n+0000c050: e280 9866 696c 6c63 6f6c 6f72 e280 992c ...fillcolor...,\n+0000c060: 20e2 8098 6669 6c6c 7374 796c 65e2 8099 ...fillstyle...\n+0000c070: 2c0a e280 986c 696e 6563 6f6c 6f72 e280 ,....linecolor..\n+0000c080: 992c 20e2 8098 6c69 6e65 7374 796c 65e2 ., ...linestyle.\n+0000c090: 8099 2c20 e280 986c 696e 6577 6964 7468 .., ...linewidth\n+0000c0a0: e280 992c 20e2 8098 6f70 6163 6974 79e2 ..., ...opacity.\n+0000c0b0: 8099 2c20 e280 9873 686f 7770 6f69 6e74 .., ...showpoint\n+0000c0c0: 73e2 8099 2c0a e280 9873 7472 6f6b 656f s...,....strokeo\n+0000c0d0: 7061 6369 7479 e280 992c 2061 6e64 20e2 pacity..., and .\n+0000c0e0: 8098 7472 616e 7370 616c 7068 61e2 8099 ..transpalpha...\n+0000c0f0: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n+0000c100: 682e 696e 666f 2c20 204e 6f64 653a 2054 h.info, Node: T\n+0000c110: 696b 5a2f 5047 4620 6f70 7469 6f6e 732c ikZ/PGF options,\n+0000c120: 2020 4e65 7874 3a20 446f 7473 2069 6e20 Next: Dots in \n+0000c130: 5469 6b5a 2f50 4746 2c20 2050 7265 763a TikZ/PGF, Prev:\n+0000c140: 2050 5354 7269 636b 7320 6f70 7469 6f6e PSTricks option\n+0000c150: 732c 2020 5570 3a20 4f70 7469 6f6e 730a s, Up: Options.\n+0000c160: 0a33 2e31 2e35 2e32 20e2 8098 5469 6b5a .3.1.5.2 ...TikZ\n+0000c170: 2f50 4746 e280 9920 6f70 7469 6f6e 730a /PGF... options.\n+0000c180: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+0000c190: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a e280 9854 ...............T\n+0000c1a0: 696b 5a2f 5047 46e2 8099 206f 7074 696f ikZ/PGF... optio\n+0000c1b0: 6e73 2061 7265 2068 616e 646c 6564 206d ns are handled m\n+0000c1c0: 7563 6820 6173 2066 6f72 20e2 8098 5053 uch as for ...PS\n+0000c1d0: 5472 6963 6b73 e280 992e 2020 5468 6f75 Tricks.... 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To draw a re\n+0000c2a0: 642c 2075 6c74 7261 2d74 6869 636b 206c d, ultra-thick l\n+0000c2b0: 696e 6520 696e 0ae2 8098 736b 6574 6368 ine in....sketch\n+0000c2c0: e280 992c 2074 6865 2066 6f72 6d20 6973 ..., the form is\n+0000c2d0: 0a20 206c 696e 655b 6472 6177 3d72 6564 . line[draw=red\n+0000c2e0: 2c73 7479 6c65 3d75 6c74 7261 2074 6869 ,style=ultra thi\n+0000c2f0: 636b 5d28 302c 3029 2831 2c31 290a 0a20 ck](0,0)(1,1).. \n+0000c300: 2020 4a75 7374 2061 7320 666f 7220 e280 Just as for ..\n+0000c310: 9850 5354 7269 636b 73e2 8099 2c20 7768 .PSTricks..., wh\n+0000c320: 656e 2061 20e2 8098 706f 6c79 676f 6ee2 en a ...polygon.\n+0000c330: 8099 2068 6173 206f 7074 696f 6e73 2066 .. has options f\n+0000c340: 6f72 2062 6f74 6820 6974 730a 6661 6365 or both its.face\n+0000c350: 2061 6e64 2069 7473 2065 6467 6573 2c20 and its edges, \n+0000c360: 616e 6420 7468 6520 706f 6c79 676f 6e20 and the polygon \n+0000c370: 6973 2073 706c 6974 2062 7920 7468 6520 is split by the \n+0000c380: 6869 6464 656e 2073 7572 6661 6365 0a61 hidden surface.a\n+0000c390: 6c67 6f72 6974 686d 2c20 e280 9873 6b65 lgorithm, ...ske\n+0000c3a0: 7463 68e2 8099 206d 7573 7420 636f 7079 tch... must copy\n+0000c3b0: 2074 6865 2065 6467 6520 6f70 7469 6f6e the edge option\n+0000c3c0: 7320 746f 20e2 8098 7073 6c69 6e65 e280 s to ...psline..\n+0000c3d0: 9973 2066 6f72 2074 6865 2065 6467 650a .s for the edge.\n+0000c3e0: 7365 676d 656e 7473 2061 6e64 2074 6865 segments and the\n+0000c3f0: 2066 6163 6520 6f70 7469 6f6e 7320 746f face options to\n+0000c400: 20e2 8098 7073 706f 6c79 676f 6ee2 8099 ...pspolygon...\n+0000c410: 732e 2020 e280 9854 696b 5a2f 5047 46e2 s. ...TikZ/PGF.\n+0000c420: 8099 206f 7074 696f 6e73 206b 6e6f 776e .. options known\n+0000c430: 0a74 6f20 e280 9873 6b65 7463 68e2 8099 .to ...sketch...\n+0000c440: 2066 6f72 2070 7572 706f 7365 7320 6f66 for purposes of\n+0000c450: 2074 6869 7320 7370 6c69 7474 696e 6720 this splitting \n+0000c460: 6f70 6572 6174 696f 6e20 696e 636c 7564 operation includ\n+0000c470: 6520 e280 9861 7272 6f77 73e2 8099 2c0a e ...arrows...,.\n+0000c480: e280 9863 6170 e280 992c 20e2 8098 636f ...cap..., ...co\n+0000c490: 6c6f 72e2 8099 2c20 e280 9864 6173 6820 lor..., ...dash \n+0000c4a0: 7061 7474 6572 6ee2 8099 2c20 e280 9864 pattern..., ...d\n+0000c4b0: 6173 6820 7068 6173 65e2 8099 2c20 e280 ash phase..., ..\n+0000c4c0: 9864 6f75 626c 65e2 8099 2c20 e280 9864 .double..., ...d\n+0000c4d0: 6f75 626c 650a 6469 7374 616e 6365 e280 ouble.distance..\n+0000c4e0: 992c 20e2 8098 6472 6177 e280 992c 20e2 ., ...draw..., .\n+0000c4f0: 8098 6472 6177 206f 7061 6369 7479 e280 ..draw opacity..\n+0000c500: 992c 20e2 8098 6669 6c6c e280 992c 20e2 ., ...fill..., .\n+0000c510: 8098 6669 6c6c 206f 7061 6369 7479 e280 ..fill opacity..\n+0000c520: 992c 20e2 8098 6a6f 696e e280 992c 20e2 ., ...join..., .\n+0000c530: 8098 6c69 6e65 0a77 6964 7468 e280 992c ..line.width...,\n+0000c540: 20e2 8098 6d69 7465 7220 6c69 6d69 74e2 ...miter limit.\n+0000c550: 8099 2c20 e280 9870 6174 7465 726e e280 .., ...pattern..\n+0000c560: 992c 20e2 8098 7061 7474 6572 6e20 636f ., ...pattern co\n+0000c570: 6c6f 72e2 8099 2c20 616e 6420 e280 9873 lor..., and ...s\n+0000c580: 7479 6c65 e280 992e 0a0a 2020 2054 6865 tyle...... 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Val\n+0000c600: 7565 7320 6b6e 6f77 6e20 746f 20e2 8098 ues known to ...\n+0000c610: 736b 6574 6368 e280 9920 696e 636c 7564 sketch... includ\n+0000c620: 650a e280 9864 6173 6865 64e2 8099 2c20 e....dashed..., \n+0000c630: e280 9864 656e 7365 6c79 2064 6173 6865 ...densely dashe\n+0000c640: 64e2 8099 2c20 e280 9864 656e 7365 6c79 d..., ...densely\n+0000c650: 2064 6f74 7465 64e2 8099 2c20 e280 9864 dotted..., ...d\n+0000c660: 6f74 7465 64e2 8099 2c20 e280 9864 6f75 otted..., ...dou\n+0000c670: 626c 65e2 8099 2c0a e280 986c 6f6f 7365 ble...,....loose\n+0000c680: 6c79 2064 6173 6865 64e2 8099 2c20 e280 ly dashed..., ..\n+0000c690: 986c 6f6f 7365 6c79 2064 6f74 7465 64e2 .loosely dotted.\n+0000c6a0: 8099 2c20 e280 986e 6561 726c 7920 6f70 .., ...nearly op\n+0000c6b0: 6171 7565 e280 992c 20e2 8098 6e65 6172 aque..., ...near\n+0000c6c0: 6c79 0a74 7261 6e73 7061 7265 6e74 e280 ly.transparent..\n+0000c6d0: 992c 20e2 8098 7365 6d69 7468 6963 6be2 ., ...semithick.\n+0000c6e0: 8099 2c20 e280 9873 656d 6974 7261 6e73 .., ...semitrans\n+0000c6f0: 7061 7265 6e74 e280 992c 20e2 8098 736f parent..., ...so\n+0000c700: 6c69 64e2 8099 2c20 e280 9874 6869 636b lid..., ...thick\n+0000c710: e280 992c 20e2 8098 7468 696e e280 992c ..., ...thin...,\n+0000c720: 0ae2 8098 7472 616e 7370 6172 656e 74e2 ....transparent.\n+0000c730: 8099 2c20 e280 9875 6c74 7261 206e 6561 .., ...ultra nea\n+0000c740: 726c 7920 7472 616e 7370 6172 656e 74e2 rly transparent.\n+0000c750: 8099 2c20 e280 9875 6c74 7261 2074 6869 .., ...ultra thi\n+0000c760: 636b e280 992c 20e2 8098 756c 7472 6120 ck..., ...ultra \n+0000c770: 7468 696e e280 992c 0ae2 8098 7665 7279 thin...,....very\n+0000c780: 206e 6561 726c 7920 7472 616e 7370 6172 nearly transpar\n+0000c790: 656e 74e2 8099 2c20 e280 9876 6572 7920 ent..., ...very \n+0000c7a0: 7468 6963 6be2 8099 2c20 616e 6420 e280 thick..., and ..\n+0000c7b0: 9876 6572 7920 7468 696e e280 992e 0a0a .very thin......\n+0000c7c0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+0000c7d0: 6e66 6f2c 2020 4e6f 6465 3a20 446f 7473 nfo, Node: Dots\n+0000c7e0: 2069 6e20 5469 6b5a 2f50 4746 2c20 204e in TikZ/PGF, N\n+0000c7f0: 6578 743a 2054 696b 5a2f 5047 4620 7573 ext: TikZ/PGF us\n+0000c800: 6572 2d64 6566 696e 6564 2073 7479 6c65 er-defined style\n+0000c810: 732c 2020 5072 6576 3a20 5469 6b5a 2f50 s, Prev: TikZ/P\n+0000c820: 4746 206f 7074 696f 6e73 2c20 2055 703a GF options, Up:\n+0000c830: 204f 7074 696f 6e73 0a0a 332e 312e 352e Options..3.1.5.\n+0000c840: 3320 446f 7473 2069 6e20 e280 9854 696b 3 Dots in ...Tik\n+0000c850: 5a2f 5047 46e2 8099 0a2e 2e2e 2e2e 2e2e Z/PGF...........\n 0000c860: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000c870: 2e2e 2e2e 2e0a 0ae2 8098 5469 6b5a 2f50 ..........TikZ/P\n-0000c880: 4746 e280 9920 646f 6573 206e 6f74 2068 GF... does not h\n-0000c890: 6176 6520 6120 e280 9864 6f74 73e2 8099 ave a ...dots...\n-0000c8a0: 2063 6f6d 6d61 6e64 2061 7320 646f 6573 command as does\n-0000c8b0: 2050 5354 7269 636b 732e 2020 496e 7374 PSTricks. Inst\n-0000c8c0: 6561 642c 0ae2 8098 536b 6574 6368 e280 ead,....Sketch..\n-0000c8d0: 9920 656d 6974 7320 646f 7473 2061 7320 . emits dots as \n-0000c8e0: e280 9866 696c 6c64 7261 77e2 8099 2063 ...filldraw... c\n-0000c8f0: 6972 636c 6573 2e20 2054 6865 2064 6961 ircles. The dia\n-0000c900: 6d65 7465 7220 6d61 7920 6265 2073 6574 meter may be set\n-0000c910: 0a75 7369 6e67 2074 6865 206f 7074 696f .using the optio\n-0000c920: 6e20 e280 9864 6f74 7369 7a65 e280 9920 n ...dotsize... \n-0000c930: 626f 7272 6f77 6564 2066 726f 6d20 5053 borrowed from PS\n-0000c940: 5472 6963 6b73 2e20 2054 6865 20e2 8098 Tricks. The ...\n-0000c950: 646f 7473 697a 65e2 8099 206f 7074 696f dotsize... optio\n-0000c960: 6e0a 7769 6c6c 2062 6520 7265 6d6f 7665 n.will be remove\n-0000c970: 6420 6672 6f6d 2074 6865 206f 7074 696f d from the optio\n-0000c980: 6e20 6c69 7374 2069 6e20 7468 6520 6f75 n list in the ou\n-0000c990: 7470 7574 20e2 8098 6669 6c6c 6472 6177 tput ...filldraw\n-0000c9a0: e280 9920 636f 6d6d 616e 642e 0a4f 7468 ... command..Oth\n-0000c9b0: 6572 206f 7074 696f 6e73 2077 6f72 6b20 er options work \n-0000c9c0: 696e 2074 6865 2065 7870 6563 7465 6420 in the expected \n-0000c9d0: 7761 792e 2020 466f 7220 6578 616d 706c way. For exampl\n-0000c9e0: 652c 20e2 8098 6669 6c6c e280 9920 7365 e, ...fill... se\n-0000c9f0: 7473 2066 696c 6c0a 636f 6c6f 7220 616e ts fill.color an\n-0000ca00: 6420 e280 9863 6f6c 6f72 e280 9920 7365 d ...color... se\n-0000ca10: 7473 206c 696e 6520 636f 6c6f 7220 6f66 ts line color of\n-0000ca20: 2074 6865 2063 6972 636c 6573 2e0a 0a1f the circles....\n-0000ca30: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-0000ca40: 666f 2c20 204e 6f64 653a 2054 696b 5a2f fo, Node: TikZ/\n-0000ca50: 5047 4620 7573 6572 2d64 6566 696e 6564 PGF user-defined\n-0000ca60: 2073 7479 6c65 732c 2020 4e65 7874 3a20 styles, Next: \n-0000ca70: 5472 616e 7370 6172 656e 6379 2c20 2050 Transparency, P\n-0000ca80: 7265 763a 2044 6f74 7320 696e 2054 696b rev: Dots in Tik\n-0000ca90: 5a2f 5047 462c 2020 5570 3a20 4f70 7469 Z/PGF, Up: Opti\n-0000caa0: 6f6e 730a 0a33 2e31 2e35 2e34 20e2 8098 ons..3.1.5.4 ...\n-0000cab0: 5469 6b5a 2f50 4746 e280 9920 7573 6572 TikZ/PGF... user\n-0000cac0: 2d64 6566 696e 6564 2073 7479 6c65 730a -defined styles.\n+0000c870: 2e2e 2e0a 0ae2 8098 5469 6b5a 2f50 4746 ........TikZ/PGF\n+0000c880: e280 9920 646f 6573 206e 6f74 2068 6176 ... does not hav\n+0000c890: 6520 6120 e280 9864 6f74 73e2 8099 2063 e a ...dots... c\n+0000c8a0: 6f6d 6d61 6e64 2061 7320 646f 6573 2050 ommand as does P\n+0000c8b0: 5354 7269 636b 732e 2020 496e 7374 6561 STricks. Instea\n+0000c8c0: 642c 0ae2 8098 536b 6574 6368 e280 9920 d,....Sketch... \n+0000c8d0: 656d 6974 7320 646f 7473 2061 7320 e280 emits dots as ..\n+0000c8e0: 9866 696c 6c64 7261 77e2 8099 2063 6972 .filldraw... cir\n+0000c8f0: 636c 6573 2e20 2054 6865 2064 6961 6d65 cles. The diame\n+0000c900: 7465 7220 6d61 7920 6265 2073 6574 0a75 ter may be set.u\n+0000c910: 7369 6e67 2074 6865 206f 7074 696f 6e20 sing the option \n+0000c920: e280 9864 6f74 7369 7a65 e280 9920 626f ...dotsize... bo\n+0000c930: 7272 6f77 6564 2066 726f 6d20 5053 5472 rrowed from PSTr\n+0000c940: 6963 6b73 2e20 2054 6865 20e2 8098 646f icks. The ...do\n+0000c950: 7473 697a 65e2 8099 206f 7074 696f 6e0a tsize... option.\n+0000c960: 7769 6c6c 2062 6520 7265 6d6f 7665 6420 will be removed \n+0000c970: 6672 6f6d 2074 6865 206f 7074 696f 6e20 from the option \n+0000c980: 6c69 7374 2069 6e20 7468 6520 6f75 7470 list in the outp\n+0000c990: 7574 20e2 8098 6669 6c6c 6472 6177 e280 ut ...filldraw..\n+0000c9a0: 9920 636f 6d6d 616e 642e 0a4f 7468 6572 . command..Other\n+0000c9b0: 206f 7074 696f 6e73 2077 6f72 6b20 696e options work in\n+0000c9c0: 2074 6865 2065 7870 6563 7465 6420 7761 the expected wa\n+0000c9d0: 792e 2020 466f 7220 6578 616d 706c 652c y. For example,\n+0000c9e0: 20e2 8098 6669 6c6c e280 9920 7365 7473 ...fill... sets\n+0000c9f0: 2066 696c 6c0a 636f 6c6f 7220 616e 6420 fill.color and \n+0000ca00: e280 9863 6f6c 6f72 e280 9920 7365 7473 ...color... sets\n+0000ca10: 206c 696e 6520 636f 6c6f 7220 6f66 2074 line color of t\n+0000ca20: 6865 2063 6972 636c 6573 2e0a 0a1f 0a46 he circles.....F\n+0000ca30: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+0000ca40: 2c20 204e 6f64 653a 2054 696b 5a2f 5047 , Node: TikZ/PG\n+0000ca50: 4620 7573 6572 2d64 6566 696e 6564 2073 F user-defined s\n+0000ca60: 7479 6c65 732c 2020 4e65 7874 3a20 5472 tyles, Next: Tr\n+0000ca70: 616e 7370 6172 656e 6379 2c20 2050 7265 ansparency, Pre\n+0000ca80: 763a 2044 6f74 7320 696e 2054 696b 5a2f v: Dots in TikZ/\n+0000ca90: 5047 462c 2020 5570 3a20 4f70 7469 6f6e PGF, Up: Option\n+0000caa0: 730a 0a33 2e31 2e35 2e34 20e2 8098 5469 s..3.1.5.4 ...Ti\n+0000cab0: 6b5a 2f50 4746 e280 9920 7573 6572 2d64 kZ/PGF... user-d\n+0000cac0: 6566 696e 6564 2073 7479 6c65 730a 2e2e efined styles...\n 0000cad0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n 0000cae0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000caf0: 2e2e 2e2e 2e2e 0a0a e280 9854 696b 5a2f ...........TikZ/\n-0000cb00: 5047 46e2 8099 2061 6c6c 6f77 7320 6e61 PGF... allows na\n-0000cb10: 6d65 6420 7374 796c 6573 2064 6566 696e med styles defin\n-0000cb20: 6564 2062 7920 7468 6520 7573 6572 2c20 ed by the user, \n-0000cb30: 666f 7220 6578 616d 706c 650a 2020 5c74 for example. \\t\n-0000cb40: 696b 7a73 7479 6c65 7b6d 7970 6f6c 7967 ikzstyle{mypolyg\n-0000cb50: 6f6e 7374 796c 657d 203d 205b 6669 6c6c onstyle} = [fill\n-0000cb60: 3d62 6c75 6521 3230 2c66 696c 6c20 6f70 =blue!20,fill op\n-0000cb70: 6163 6974 793d 302e 385d 2020 0a20 205c acity=0.8] . \\\n-0000cb80: 7469 6b7a 7374 796c 657b 6d79 6c69 6e65 tikzstyle{myline\n-0000cb90: 7374 796c 657d 203d 205b 7265 6421 3230 style} = [red!20\n-0000cba0: 2c64 6173 6865 645d 0a53 696e 6365 20e2 ,dashed].Since .\n-0000cbb0: 8098 736b 6574 6368 e280 9920 6861 7320 ..sketch... has \n-0000cbc0: 6e6f 2069 6e66 6f72 6d61 7469 6f6e 206f no information o\n-0000cbd0: 6e20 7468 6520 636f 6e74 656e 7473 206f n the contents o\n-0000cbe0: 6620 7375 6368 2073 7479 6c65 732c 2069 f such styles, i\n-0000cbf0: 740a 6f6d 6974 7320 7468 656d 2065 6e74 t.omits them ent\n-0000cc00: 6972 656c 7920 6672 6f6d 206c 696e 6573 irely from lines\n-0000cc10: 2c20 706f 6c79 676f 6e73 2c20 616e 6420 , polygons, and \n-0000cc20: 7468 6569 7220 6564 6765 7320 6475 7269 their edges duri\n-0000cc30: 6e67 206f 7074 696f 6e0a 7370 6c69 7474 ng option.splitt\n-0000cc40: 696e 672e 2020 466f 7220 6578 616d 706c ing. For exampl\n-0000cc50: 652c 0a20 2070 6f6c 7967 6f6e 5b73 7479 e,. polygon[sty\n-0000cc60: 6c65 3d6d 7970 6f6c 7967 6f6e 7374 796c le=mypolygonstyl\n-0000cc70: 652c 7374 796c 653d 7468 6963 6b5d 2830 e,style=thick](0\n-0000cc80: 2c30 2c31 2928 312c 302c 3029 2830 2c31 ,0,1)(1,0,0)(0,1\n-0000cc90: 2c30 290a 2020 6c69 6e65 5b73 7479 6c65 ,0). line[style\n-0000cca0: 3d6d 796c 696e 6573 7479 6c65 5d28 2d31 =mylinestyle](-1\n-0000ccb0: 2c2d 312c 2d31 2928 322c 322c 3229 0a70 ,-1,-1)(2,2,2).p\n-0000ccc0: 726f 6475 6365 7320 7468 6520 e280 9854 roduces the ...T\n-0000ccd0: 696b 5ae2 8099 206f 7574 7075 740a 2020 ikZ... output. \n-0000cce0: 5c64 7261 7728 2d31 2c2d 3129 2d2d 282e \\draw(-1,-1)--(.\n-0000ccf0: 3333 332c 2e33 3333 293b 0a20 205c 6669 333,.333);. \\fi\n-0000cd00: 6c6c 6472 6177 5b74 6869 636b 2c66 696c lldraw[thick,fil\n-0000cd10: 6c3d 7768 6974 655d 2830 2c30 292d 2d28 l=white](0,0)--(\n-0000cd20: 312c 3029 2d2d 2830 2c31 292d 2d63 7963 1,0)--(0,1)--cyc\n-0000cd30: 6c65 3b0a 2020 5c64 7261 7728 2e33 3333 le;. \\draw(.333\n-0000cd40: 2c2e 3333 3329 2d2d 2832 2c32 293b 0a4e ,.333)--(2,2);.N\n-0000cd50: 6f74 6520 7468 6174 2074 6865 2075 7365 ote that the use\n-0000cd60: 722d 6465 6669 6e65 6420 7374 796c 6573 r-defined styles\n-0000cd70: 2061 7265 206e 6f74 2070 7265 7365 6e74 are not present\n-0000cd80: 2e20 2053 6b65 7463 6820 616c 736f 2069 . Sketch also i\n-0000cd90: 7373 7565 730a 7761 726e 696e 6773 3a0a ssues.warnings:.\n-0000cda0: 2020 7761 726e 696e 672c 2075 6e6b 6e6f warning, unkno\n-0000cdb0: 776e 2070 6f6c 7967 6f6e 206f 7074 696f wn polygon optio\n-0000cdc0: 6e20 7374 796c 653d 6d79 706f 6c79 676f n style=mypolygo\n-0000cdd0: 6e73 7479 6c65 2077 696c 6c20 6265 2069 nstyle will be i\n-0000cde0: 676e 6f72 6564 0a20 2077 6172 6e69 6e67 gnored. warning\n-0000cdf0: 2c20 756e 6b6e 6f77 6e20 6c69 6e65 206f , unknown line o\n-0000ce00: 7074 696f 6e20 7374 796c 653d 6d79 6c69 ption style=myli\n-0000ce10: 6e65 7374 796c 6520 7769 6c6c 2062 6520 nestyle will be \n-0000ce20: 6967 6e6f 7265 640a 0a20 2020 5468 6520 ignored.. The \n-0000ce30: 7265 6d65 6479 2069 7320 746f 2073 7461 remedy is to sta\n-0000ce40: 7465 2065 7870 6c69 6369 746c 7920 7768 te explicitly wh\n-0000ce50: 6574 6865 7220 6120 7573 6572 2d64 6566 ether a user-def\n-0000ce60: 696e 6564 2073 7479 6c65 2073 686f 756c ined style shoul\n-0000ce70: 640a 6265 2061 7474 6368 6564 2074 6f20 d.be attched to \n-0000ce80: 706f 6c79 676f 6e73 206f 7220 6c69 6e65 polygons or line\n-0000ce90: 7320 696e 2074 6865 20e2 8098 5469 6b5a s in the ...TikZ\n-0000cea0: e280 9920 6f75 7470 7574 2075 7369 6e67 ... output using\n-0000ceb0: 0a5f 7073 6575 646f 2d6f 7074 696f 6e73 ._pseudo-options\n-0000cec0: 5f20 e280 9866 696c 6c20 7374 796c 65e2 _ ...fill style.\n-0000ced0: 8099 2061 6e64 20e2 8098 6c69 6e65 2073 .. and ...line s\n-0000cee0: 7479 6c65 e280 992c 0a20 2070 6f6c 7967 tyle...,. polyg\n-0000cef0: 6f6e 5b66 696c 6c20 7374 796c 653d 6d79 on[fill style=my\n-0000cf00: 706f 6c79 676f 6e73 7479 6c65 2c73 7479 polygonstyle,sty\n-0000cf10: 6c65 3d74 6869 636b 5d28 302c 302c 3129 le=thick](0,0,1)\n-0000cf20: 2831 2c30 2c30 2928 302c 312c 3029 0a20 (1,0,0)(0,1,0). \n-0000cf30: 206c 696e 655b 6c69 6e65 2073 7479 6c65 line[line style\n-0000cf40: 3d6d 796c 696e 6573 7479 6c65 5d28 2d31 =mylinestyle](-1\n-0000cf50: 2c2d 312c 2d31 2928 322c 322c 3229 0a4e ,-1,-1)(2,2,2).N\n-0000cf60: 6f77 2c20 7468 6520 6f75 7470 7574 2069 ow, the output i\n-0000cf70: 730a 2020 5c64 7261 775b 6d79 6c69 6e65 s. \\draw[myline\n-0000cf80: 7374 796c 655d 282d 312c 2d31 292d 2d28 style](-1,-1)--(\n-0000cf90: 2e33 3333 2c2e 3333 3329 3b0a 2020 5c66 .333,.333);. \\f\n-0000cfa0: 696c 6c64 7261 775b 6d79 706f 6c79 676f illdraw[mypolygo\n-0000cfb0: 6e73 7479 6c65 2c74 6869 636b 5d28 302c nstyle,thick](0,\n-0000cfc0: 3029 2d2d 2831 2c30 292d 2d28 302c 3129 0)--(1,0)--(0,1)\n-0000cfd0: 2d2d 6379 636c 653b 0a20 205c 6472 6177 --cycle;. \\draw\n-0000cfe0: 5b6d 796c 696e 6573 7479 6c65 5d28 2e33 [mylinestyle](.3\n-0000cff0: 3333 2c2e 3333 3329 2d2d 2832 2c32 293b 33,.333)--(2,2);\n-0000d000: 0a0a 2020 2041 2075 7365 6675 6c20 7465 .. A useful te\n-0000d010: 6368 6e69 7175 6520 6973 2074 6f20 696e chnique is to in\n-0000d020: 636c 7564 6520 7573 6572 2d64 6566 696e clude user-defin\n-0000d030: 6564 2073 7479 6c65 2064 6566 696e 6974 ed style definit\n-0000d040: 696f 6e73 2069 6e0a e280 9873 6b65 7463 ions in....sketc\n-0000d050: 68e2 8099 2063 6f64 6520 6173 20e2 8098 h... code as ...\n-0000d060: 7370 6563 6961 6ce2 8099 7320 7769 7468 special...s with\n-0000d070: 206f 7074 696f 6e20 e280 985b 6c61 793d option ...[lay=\n-0000d080: 756e 6465 725d e280 9920 746f 2065 6e73 under]... to ens\n-0000d090: 7572 6520 7468 6174 2074 6865 0a73 7479 ure that the.sty\n-0000d0a0: 6c65 7320 6172 6520 656d 6974 7465 6420 les are emitted \n-0000d0b0: 6669 7273 7420 696e 2074 6865 206f 7574 first in the out\n-0000d0c0: 7075 742c 2062 6566 6f72 6520 616e 7920 put, before any \n-0000d0d0: 7573 6573 206f 6620 7468 6520 7374 796c uses of the styl\n-0000d0e0: 650a 6e61 6d65 732e 2020 2831 2920 2046 e.names. (1) F\n-0000d0f0: 6f72 2065 7861 6d70 6c65 2c0a 2020 7370 or example,. sp\n-0000d100: 6563 6961 6c7c 5c74 696b 7a73 7479 6c65 ecial|\\tikzstyle\n-0000d110: 7b6d 7970 6f6c 7967 6f6e 7374 796c 657d {mypolygonstyle}\n-0000d120: 203d 205b 6669 6c6c 3d62 6c75 6521 3230 = [fill=blue!20\n-0000d130: 2c66 696c 6c20 6f70 6163 6974 793d 302e ,fill opacity=0.\n-0000d140: 385d 7c5b 6c61 793d 756e 6465 725d 0a20 8]|[lay=under]. \n-0000d150: 2073 7065 6369 616c 7c5c 7469 6b7a 7374 special|\\tikzst\n-0000d160: 796c 657b 6d79 6c69 6e65 7374 796c 657d yle{mylinestyle}\n-0000d170: 203d 205b 7265 6421 3230 2c64 6173 6865 = [red!20,dashe\n-0000d180: 645d 7c5b 6c61 793d 756e 6465 725d 0a54 d]|[lay=under].T\n-0000d190: 6865 2061 7574 686f 7220 6973 2072 6573 he author is res\n-0000d1a0: 706f 6e73 6962 6c65 2066 6f72 2075 7369 ponsible for usi\n-0000d1b0: 6e67 2074 6865 206b 6579 2c20 e280 986c ng the key, ...l\n-0000d1c0: 696e 6520 7374 796c 65e2 8099 206f 7220 ine style... or \n-0000d1d0: e280 9866 696c 6c0a 7374 796c 65e2 8099 ...fill.style...\n-0000d1e0: 2c20 7468 6174 206d 6174 6368 6573 2074 , that matches t\n-0000d1f0: 6865 2063 6f6e 7465 6e74 206f 6620 7468 he content of th\n-0000d200: 6520 7374 796c 6520 6465 6669 6e69 7469 e style definiti\n-0000d210: 6f6e 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d on... --------\n-0000d220: 2d2d 2046 6f6f 746e 6f74 6573 202d 2d2d -- Footnotes ---\n-0000d230: 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831 2920 -------.. (1) \n-0000d240: 5468 6973 2063 6c65 7665 7220 7472 6963 This clever tric\n-0000d250: 6b20 6973 2064 7565 2074 6f20 4b6a 656c k is due to Kjel\n-0000d260: 6c20 4d61 676e 6520 4661 7573 6b65 2e0a l Magne Fauske..\n-0000d270: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-0000d280: 696e 666f 2c20 204e 6f64 653a 2054 7261 info, Node: Tra\n-0000d290: 6e73 7061 7265 6e63 792c 2020 4e65 7874 nsparency, Next\n-0000d2a0: 3a20 496e 7465 726e 616c 206f 7074 696f : Internal optio\n-0000d2b0: 6e73 2c20 2050 7265 763a 2054 696b 5a2f ns, Prev: TikZ/\n-0000d2c0: 5047 4620 7573 6572 2d64 6566 696e 6564 PGF user-defined\n-0000d2d0: 2073 7479 6c65 732c 2020 5570 3a20 4f70 styles, Up: Op\n-0000d2e0: 7469 6f6e 730a 0a33 2e31 2e35 2e35 2054 tions..3.1.5.5 T\n-0000d2f0: 7261 6e73 7061 7265 6e63 790a 2e2e 2e2e ransparency.....\n-0000d300: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000d310: 0a0a 426f 7468 20e2 8098 5053 5472 6963 ..Both ...PSTric\n-0000d320: 6b73 e280 9920 616e 6420 e280 9854 696b ks... and ...Tik\n-0000d330: 5a2f 5047 46e2 8099 2073 7570 706f 7274 Z/PGF... support\n-0000d340: 2070 6f6c 7967 6f6e 206f 7074 696f 6e73 polygon options\n-0000d350: 2074 6861 7420 6861 7665 2074 6865 0a65 that have the.e\n-0000d360: 6666 6563 7420 6f66 206d 616b 696e 6720 ffect of making \n-0000d370: 7468 6520 706f 6c79 676f 6e20 6170 7065 the polygon appe\n-0000d380: 6172 2074 7261 6e73 7061 7265 6e74 2e20 ar transparent. \n-0000d390: 2046 6f72 20e2 8098 5053 5472 6963 6b73 For ...PSTricks\n-0000d3a0: e280 992c 0a6b 6579 776f 7264 20e2 8098 ...,.keyword ...\n-0000d3b0: 7472 616e 7370 616c 7068 61e2 8099 2077 transpalpha... w\n-0000d3c0: 6173 2075 7365 6420 6475 7269 6e67 2069 as used during i\n-0000d3d0: 6e69 7469 616c 2064 6576 656c 6f70 6d65 nitial developme\n-0000d3e0: 6e74 206f 660a 7472 616e 7370 6172 656e nt of.transparen\n-0000d3f0: 6379 2066 6561 7475 7265 732c 2061 6e64 cy features, and\n-0000d400: 20e2 8098 6f70 6163 6974 79e2 8099 2077 ...opacity... w\n-0000d410: 6173 2061 646f 7074 6564 206c 6174 6572 as adopted later\n-0000d420: 2e20 20e2 8098 536b 6574 6368 e280 9920 . ...Sketch... \n-0000d430: 686f 6e6f 7273 0a62 6f74 682e 2020 e280 honors.both. ..\n-0000d440: 9854 696b 5a2f 5047 46e2 8099 2075 7365 .TikZ/PGF... use\n-0000d450: 7320 e280 986f 7061 6369 7479 e280 9920 s ...opacity... \n-0000d460: 6f6e 6c79 2e20 2057 6865 6e20 7472 616e only. When tran\n-0000d470: 7370 6172 656e 7420 706f 6c79 676f 6e73 sparent polygons\n-0000d480: 2061 7265 2069 6e0a 7468 6520 666f 7265 are in.the fore\n-0000d490: 6772 6f75 6e64 2c20 6f62 6a65 6374 7320 ground, objects \n-0000d4a0: 6265 6869 6e64 2074 6865 6d20 2864 7261 behind them (dra\n-0000d4b0: 776e 2065 6172 6c69 6572 2920 6172 6520 wn earlier) are \n-0000d4c0: 7669 7369 626c 6520 7769 7468 0a63 6f6c visible with.col\n-0000d4d0: 6f72 2073 7562 6475 6564 2061 6e64 2074 or subdued and t\n-0000d4e0: 696e 7465 642e 2020 5468 6520 6869 6464 inted. The hidd\n-0000d4f0: 656e 2073 7572 6661 6365 2061 6c67 6f72 en surface algor\n-0000d500: 6974 686d 206f 6620 e280 9873 6b65 7463 ithm of ...sketc\n-0000d510: 68e2 8099 0a77 6f72 6b73 2077 656c 6c20 h....works well \n-0000d520: 7769 7468 2073 7563 6820 7472 616e 7370 with such transp\n-0000d530: 6172 656e 7420 706f 6c79 676f 6e73 2e0a arent polygons..\n-0000d540: 0a20 2020 4e6f 7465 2074 6861 7420 6375 . Note that cu\n-0000d550: 6c6c 3d66 616c 7365 206d 7573 7420 6265 ll=false must be\n-0000d560: 2075 7365 6420 666f 7220 7265 6172 2d66 used for rear-f\n-0000d570: 6163 696e 6720 706f 6c79 676f 6e73 2074 acing polygons t\n-0000d580: 6f20 6265 0a76 6973 6962 6c65 2077 6865 o be.visible whe\n-0000d590: 6e20 706f 7369 7469 6f6e 6564 2062 6568 n positioned beh\n-0000d5a0: 696e 6420 6f74 6865 7220 7472 616e 7370 ind other transp\n-0000d5b0: 6172 656e 7420 7375 7266 6163 6573 2e0a arent surfaces..\n-0000d5c0: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-0000d5d0: 696e 666f 2c20 204e 6f64 653a 2049 6e74 info, Node: Int\n-0000d5e0: 6572 6e61 6c20 6f70 7469 6f6e 732c 2020 ernal options, \n-0000d5f0: 5072 6576 3a20 5472 616e 7370 6172 656e Prev: Transparen\n-0000d600: 6379 2c20 2055 703a 204f 7074 696f 6e73 cy, Up: Options\n-0000d610: 0a0a 332e 312e 352e 3620 496e 7465 726e ..3.1.5.6 Intern\n-0000d620: 616c 206f 7074 696f 6e73 0a2e 2e2e 2e2e al options......\n+0000caf0: 2e2e 2e2e 0a0a e280 9854 696b 5a2f 5047 .........TikZ/PG\n+0000cb00: 46e2 8099 2061 6c6c 6f77 7320 6e61 6d65 F... allows name\n+0000cb10: 6420 7374 796c 6573 2064 6566 696e 6564 d styles defined\n+0000cb20: 2062 7920 7468 6520 7573 6572 2c20 666f by the user, fo\n+0000cb30: 7220 6578 616d 706c 650a 2020 5c74 696b r example. \\tik\n+0000cb40: 7a73 7479 6c65 7b6d 7970 6f6c 7967 6f6e zstyle{mypolygon\n+0000cb50: 7374 796c 657d 203d 205b 6669 6c6c 3d62 style} = [fill=b\n+0000cb60: 6c75 6521 3230 2c66 696c 6c20 6f70 6163 lue!20,fill opac\n+0000cb70: 6974 793d 302e 385d 2020 0a20 205c 7469 ity=0.8] . \\ti\n+0000cb80: 6b7a 7374 796c 657b 6d79 6c69 6e65 7374 kzstyle{mylinest\n+0000cb90: 796c 657d 203d 205b 7265 6421 3230 2c64 yle} = [red!20,d\n+0000cba0: 6173 6865 645d 0a53 696e 6365 20e2 8098 ashed].Since ...\n+0000cbb0: 736b 6574 6368 e280 9920 6861 7320 6e6f sketch... has no\n+0000cbc0: 2069 6e66 6f72 6d61 7469 6f6e 206f 6e20 information on \n+0000cbd0: 7468 6520 636f 6e74 656e 7473 206f 6620 the contents of \n+0000cbe0: 7375 6368 2073 7479 6c65 732c 2069 740a such styles, it.\n+0000cbf0: 6f6d 6974 7320 7468 656d 2065 6e74 6972 omits them entir\n+0000cc00: 656c 7920 6672 6f6d 206c 696e 6573 2c20 ely from lines, \n+0000cc10: 706f 6c79 676f 6e73 2c20 616e 6420 7468 polygons, and th\n+0000cc20: 6569 7220 6564 6765 7320 6475 7269 6e67 eir edges during\n+0000cc30: 206f 7074 696f 6e0a 7370 6c69 7474 696e option.splittin\n+0000cc40: 672e 2020 466f 7220 6578 616d 706c 652c g. For example,\n+0000cc50: 0a20 2070 6f6c 7967 6f6e 5b73 7479 6c65 . polygon[style\n+0000cc60: 3d6d 7970 6f6c 7967 6f6e 7374 796c 652c =mypolygonstyle,\n+0000cc70: 7374 796c 653d 7468 6963 6b5d 2830 2c30 style=thick](0,0\n+0000cc80: 2c31 2928 312c 302c 3029 2830 2c31 2c30 ,1)(1,0,0)(0,1,0\n+0000cc90: 290a 2020 6c69 6e65 5b73 7479 6c65 3d6d ). line[style=m\n+0000cca0: 796c 696e 6573 7479 6c65 5d28 2d31 2c2d ylinestyle](-1,-\n+0000ccb0: 312c 2d31 2928 322c 322c 3229 0a70 726f 1,-1)(2,2,2).pro\n+0000ccc0: 6475 6365 7320 7468 6520 e280 9854 696b duces the ...Tik\n+0000ccd0: 5ae2 8099 206f 7574 7075 740a 2020 5c64 Z... output. \\d\n+0000cce0: 7261 7728 2d31 2c2d 3129 2d2d 282e 3333 raw(-1,-1)--(.33\n+0000ccf0: 332c 2e33 3333 293b 0a20 205c 6669 6c6c 3,.333);. \\fill\n+0000cd00: 6472 6177 5b74 6869 636b 2c66 696c 6c3d draw[thick,fill=\n+0000cd10: 7768 6974 655d 2830 2c30 292d 2d28 312c white](0,0)--(1,\n+0000cd20: 3029 2d2d 2830 2c31 292d 2d63 7963 6c65 0)--(0,1)--cycle\n+0000cd30: 3b0a 2020 5c64 7261 7728 2e33 3333 2c2e ;. \\draw(.333,.\n+0000cd40: 3333 3329 2d2d 2832 2c32 293b 0a4e 6f74 333)--(2,2);.Not\n+0000cd50: 6520 7468 6174 2074 6865 2075 7365 722d e that the user-\n+0000cd60: 6465 6669 6e65 6420 7374 796c 6573 2061 defined styles a\n+0000cd70: 7265 206e 6f74 2070 7265 7365 6e74 2e20 re not present. \n+0000cd80: 2053 6b65 7463 6820 616c 736f 2069 7373 Sketch also iss\n+0000cd90: 7565 730a 7761 726e 696e 6773 3a0a 2020 ues.warnings:. \n+0000cda0: 7761 726e 696e 672c 2075 6e6b 6e6f 776e warning, unknown\n+0000cdb0: 2070 6f6c 7967 6f6e 206f 7074 696f 6e20 polygon option \n+0000cdc0: 7374 796c 653d 6d79 706f 6c79 676f 6e73 style=mypolygons\n+0000cdd0: 7479 6c65 2077 696c 6c20 6265 2069 676e tyle will be ign\n+0000cde0: 6f72 6564 0a20 2077 6172 6e69 6e67 2c20 ored. warning, \n+0000cdf0: 756e 6b6e 6f77 6e20 6c69 6e65 206f 7074 unknown line opt\n+0000ce00: 696f 6e20 7374 796c 653d 6d79 6c69 6e65 ion style=myline\n+0000ce10: 7374 796c 6520 7769 6c6c 2062 6520 6967 style will be ig\n+0000ce20: 6e6f 7265 640a 0a20 2020 5468 6520 7265 nored.. The re\n+0000ce30: 6d65 6479 2069 7320 746f 2073 7461 7465 medy is to state\n+0000ce40: 2065 7870 6c69 6369 746c 7920 7768 6574 explicitly whet\n+0000ce50: 6865 7220 6120 7573 6572 2d64 6566 696e her a user-defin\n+0000ce60: 6564 2073 7479 6c65 2073 686f 756c 640a ed style should.\n+0000ce70: 6265 2061 7474 6368 6564 2074 6f20 706f be attched to po\n+0000ce80: 6c79 676f 6e73 206f 7220 6c69 6e65 7320 lygons or lines \n+0000ce90: 696e 2074 6865 20e2 8098 5469 6b5a e280 in the ...TikZ..\n+0000cea0: 9920 6f75 7470 7574 2075 7369 6e67 0a5f . output using._\n+0000ceb0: 7073 6575 646f 2d6f 7074 696f 6e73 5f20 pseudo-options_ \n+0000cec0: e280 9866 696c 6c20 7374 796c 65e2 8099 ...fill style...\n+0000ced0: 2061 6e64 20e2 8098 6c69 6e65 2073 7479 and ...line sty\n+0000cee0: 6c65 e280 992c 0a20 2070 6f6c 7967 6f6e le...,. polygon\n+0000cef0: 5b66 696c 6c20 7374 796c 653d 6d79 706f [fill style=mypo\n+0000cf00: 6c79 676f 6e73 7479 6c65 2c73 7479 6c65 lygonstyle,style\n+0000cf10: 3d74 6869 636b 5d28 302c 302c 3129 2831 =thick](0,0,1)(1\n+0000cf20: 2c30 2c30 2928 302c 312c 3029 0a20 206c ,0,0)(0,1,0). l\n+0000cf30: 696e 655b 6c69 6e65 2073 7479 6c65 3d6d ine[line style=m\n+0000cf40: 796c 696e 6573 7479 6c65 5d28 2d31 2c2d ylinestyle](-1,-\n+0000cf50: 312c 2d31 2928 322c 322c 3229 0a4e 6f77 1,-1)(2,2,2).Now\n+0000cf60: 2c20 7468 6520 6f75 7470 7574 2069 730a , the output is.\n+0000cf70: 2020 5c64 7261 775b 6d79 6c69 6e65 7374 \\draw[mylinest\n+0000cf80: 796c 655d 282d 312c 2d31 292d 2d28 2e33 yle](-1,-1)--(.3\n+0000cf90: 3333 2c2e 3333 3329 3b0a 2020 5c66 696c 33,.333);. \\fil\n+0000cfa0: 6c64 7261 775b 6d79 706f 6c79 676f 6e73 ldraw[mypolygons\n+0000cfb0: 7479 6c65 2c74 6869 636b 5d28 302c 3029 tyle,thick](0,0)\n+0000cfc0: 2d2d 2831 2c30 292d 2d28 302c 3129 2d2d --(1,0)--(0,1)--\n+0000cfd0: 6379 636c 653b 0a20 205c 6472 6177 5b6d cycle;. \\draw[m\n+0000cfe0: 796c 696e 6573 7479 6c65 5d28 2e33 3333 ylinestyle](.333\n+0000cff0: 2c2e 3333 3329 2d2d 2832 2c32 293b 0a0a ,.333)--(2,2);..\n+0000d000: 2020 2041 2075 7365 6675 6c20 7465 6368 A useful tech\n+0000d010: 6e69 7175 6520 6973 2074 6f20 696e 636c nique is to incl\n+0000d020: 7564 6520 7573 6572 2d64 6566 696e 6564 ude user-defined\n+0000d030: 2073 7479 6c65 2064 6566 696e 6974 696f style definitio\n+0000d040: 6e73 2069 6e0a e280 9873 6b65 7463 68e2 ns in....sketch.\n+0000d050: 8099 2063 6f64 6520 6173 20e2 8098 7370 .. code as ...sp\n+0000d060: 6563 6961 6ce2 8099 7320 7769 7468 206f ecial...s with o\n+0000d070: 7074 696f 6e20 e280 985b 6c61 793d 756e ption ...[lay=un\n+0000d080: 6465 725d e280 9920 746f 2065 6e73 7572 der]... to ensur\n+0000d090: 6520 7468 6174 2074 6865 0a73 7479 6c65 e that the.style\n+0000d0a0: 7320 6172 6520 656d 6974 7465 6420 6669 s are emitted fi\n+0000d0b0: 7273 7420 696e 2074 6865 206f 7574 7075 rst in the outpu\n+0000d0c0: 742c 2062 6566 6f72 6520 616e 7920 7573 t, before any us\n+0000d0d0: 6573 206f 6620 7468 6520 7374 796c 650a es of the style.\n+0000d0e0: 6e61 6d65 732e 2020 2831 2920 2046 6f72 names. (1) For\n+0000d0f0: 2065 7861 6d70 6c65 2c0a 2020 7370 6563 example,. spec\n+0000d100: 6961 6c7c 5c74 696b 7a73 7479 6c65 7b6d ial|\\tikzstyle{m\n+0000d110: 7970 6f6c 7967 6f6e 7374 796c 657d 203d ypolygonstyle} =\n+0000d120: 205b 6669 6c6c 3d62 6c75 6521 3230 2c66 [fill=blue!20,f\n+0000d130: 696c 6c20 6f70 6163 6974 793d 302e 385d ill opacity=0.8]\n+0000d140: 7c5b 6c61 793d 756e 6465 725d 0a20 2073 |[lay=under]. s\n+0000d150: 7065 6369 616c 7c5c 7469 6b7a 7374 796c pecial|\\tikzstyl\n+0000d160: 657b 6d79 6c69 6e65 7374 796c 657d 203d e{mylinestyle} =\n+0000d170: 205b 7265 6421 3230 2c64 6173 6865 645d [red!20,dashed]\n+0000d180: 7c5b 6c61 793d 756e 6465 725d 0a54 6865 |[lay=under].The\n+0000d190: 2061 7574 686f 7220 6973 2072 6573 706f author is respo\n+0000d1a0: 6e73 6962 6c65 2066 6f72 2075 7369 6e67 nsible for using\n+0000d1b0: 2074 6865 206b 6579 2c20 e280 986c 696e the key, ...lin\n+0000d1c0: 6520 7374 796c 65e2 8099 206f 7220 e280 e style... or ..\n+0000d1d0: 9866 696c 6c0a 7374 796c 65e2 8099 2c20 .fill.style..., \n+0000d1e0: 7468 6174 206d 6174 6368 6573 2074 6865 that matches the\n+0000d1f0: 2063 6f6e 7465 6e74 206f 6620 7468 6520 content of the \n+0000d200: 7374 796c 6520 6465 6669 6e69 7469 6f6e style definition\n+0000d210: 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d 2d2d ... ----------\n+0000d220: 2046 6f6f 746e 6f74 6573 202d 2d2d 2d2d Footnotes -----\n+0000d230: 2d2d 2d2d 2d0a 0a20 2020 2831 2920 5468 -----.. (1) Th\n+0000d240: 6973 2063 6c65 7665 7220 7472 6963 6b20 is clever trick \n+0000d250: 6973 2064 7565 2074 6f20 4b6a 656c 6c20 is due to Kjell \n+0000d260: 4d61 676e 6520 4661 7573 6b65 2e0a 0a1f Magne Fauske....\n+0000d270: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+0000d280: 666f 2c20 204e 6f64 653a 2054 7261 6e73 fo, Node: Trans\n+0000d290: 7061 7265 6e63 792c 2020 4e65 7874 3a20 parency, Next: \n+0000d2a0: 496e 7465 726e 616c 206f 7074 696f 6e73 Internal options\n+0000d2b0: 2c20 2050 7265 763a 2054 696b 5a2f 5047 , Prev: TikZ/PG\n+0000d2c0: 4620 7573 6572 2d64 6566 696e 6564 2073 F user-defined s\n+0000d2d0: 7479 6c65 732c 2020 5570 3a20 4f70 7469 tyles, Up: Opti\n+0000d2e0: 6f6e 730a 0a33 2e31 2e35 2e35 2054 7261 ons..3.1.5.5 Tra\n+0000d2f0: 6e73 7061 7265 6e63 790a 2e2e 2e2e 2e2e nsparency.......\n+0000d300: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a ................\n+0000d310: 426f 7468 20e2 8098 5053 5472 6963 6b73 Both ...PSTricks\n+0000d320: e280 9920 616e 6420 e280 9854 696b 5a2f ... and ...TikZ/\n+0000d330: 5047 46e2 8099 2073 7570 706f 7274 2070 PGF... support p\n+0000d340: 6f6c 7967 6f6e 206f 7074 696f 6e73 2074 olygon options t\n+0000d350: 6861 7420 6861 7665 2074 6865 0a65 6666 hat have the.eff\n+0000d360: 6563 7420 6f66 206d 616b 696e 6720 7468 ect of making th\n+0000d370: 6520 706f 6c79 676f 6e20 6170 7065 6172 e polygon appear\n+0000d380: 2074 7261 6e73 7061 7265 6e74 2e20 2046 transparent. F\n+0000d390: 6f72 20e2 8098 5053 5472 6963 6b73 e280 or ...PSTricks..\n+0000d3a0: 992c 0a6b 6579 776f 7264 20e2 8098 7472 .,.keyword ...tr\n+0000d3b0: 616e 7370 616c 7068 61e2 8099 2077 6173 anspalpha... was\n+0000d3c0: 2075 7365 6420 6475 7269 6e67 2069 6e69 used during ini\n+0000d3d0: 7469 616c 2064 6576 656c 6f70 6d65 6e74 tial development\n+0000d3e0: 206f 660a 7472 616e 7370 6172 656e 6379 of.transparency\n+0000d3f0: 2066 6561 7475 7265 732c 2061 6e64 20e2 features, and .\n+0000d400: 8098 6f70 6163 6974 79e2 8099 2077 6173 ..opacity... was\n+0000d410: 2061 646f 7074 6564 206c 6174 6572 2e20 adopted later. \n+0000d420: 20e2 8098 536b 6574 6368 e280 9920 686f ...Sketch... ho\n+0000d430: 6e6f 7273 0a62 6f74 682e 2020 e280 9854 nors.both. ...T\n+0000d440: 696b 5a2f 5047 46e2 8099 2075 7365 7320 ikZ/PGF... uses \n+0000d450: e280 986f 7061 6369 7479 e280 9920 6f6e ...opacity... on\n+0000d460: 6c79 2e20 2057 6865 6e20 7472 616e 7370 ly. When transp\n+0000d470: 6172 656e 7420 706f 6c79 676f 6e73 2061 arent polygons a\n+0000d480: 7265 2069 6e0a 7468 6520 666f 7265 6772 re in.the foregr\n+0000d490: 6f75 6e64 2c20 6f62 6a65 6374 7320 6265 ound, objects be\n+0000d4a0: 6869 6e64 2074 6865 6d20 2864 7261 776e hind them (drawn\n+0000d4b0: 2065 6172 6c69 6572 2920 6172 6520 7669 earlier) are vi\n+0000d4c0: 7369 626c 6520 7769 7468 0a63 6f6c 6f72 sible with.color\n+0000d4d0: 2073 7562 6475 6564 2061 6e64 2074 696e subdued and tin\n+0000d4e0: 7465 642e 2020 5468 6520 6869 6464 656e ted. The hidden\n+0000d4f0: 2073 7572 6661 6365 2061 6c67 6f72 6974 surface algorit\n+0000d500: 686d 206f 6620 e280 9873 6b65 7463 68e2 hm of ...sketch.\n+0000d510: 8099 0a77 6f72 6b73 2077 656c 6c20 7769 ...works well wi\n+0000d520: 7468 2073 7563 6820 7472 616e 7370 6172 th such transpar\n+0000d530: 656e 7420 706f 6c79 676f 6e73 2e0a 0a20 ent polygons... \n+0000d540: 2020 4e6f 7465 2074 6861 7420 6375 6c6c Note that cull\n+0000d550: 3d66 616c 7365 206d 7573 7420 6265 2075 =false must be u\n+0000d560: 7365 6420 666f 7220 7265 6172 2d66 6163 sed for rear-fac\n+0000d570: 696e 6720 706f 6c79 676f 6e73 2074 6f20 ing polygons to \n+0000d580: 6265 0a76 6973 6962 6c65 2077 6865 6e20 be.visible when \n+0000d590: 706f 7369 7469 6f6e 6564 2062 6568 696e positioned behin\n+0000d5a0: 6420 6f74 6865 7220 7472 616e 7370 6172 d other transpar\n+0000d5b0: 656e 7420 7375 7266 6163 6573 2e0a 0a1f ent surfaces....\n+0000d5c0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+0000d5d0: 666f 2c20 204e 6f64 653a 2049 6e74 6572 fo, Node: Inter\n+0000d5e0: 6e61 6c20 6f70 7469 6f6e 732c 2020 5072 nal options, Pr\n+0000d5f0: 6576 3a20 5472 616e 7370 6172 656e 6379 ev: Transparency\n+0000d600: 2c20 2055 703a 204f 7074 696f 6e73 0a0a , Up: Options..\n+0000d610: 332e 312e 352e 3620 496e 7465 726e 616c 3.1.5.6 Internal\n+0000d620: 206f 7074 696f 6e73 0a2e 2e2e 2e2e 2e2e options........\n 0000d630: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-0000d640: 2e2e 2e0a 0a54 6865 7265 2061 7265 2061 .....There are a\n-0000d650: 6c73 6f20 5f69 6e74 6572 6e61 6c5f 206f lso _internal_ o\n-0000d660: 7074 696f 6e73 2075 7365 6420 6f6e 6c79 ptions used only\n-0000d670: 2062 7920 e280 9873 6b65 7463 68e2 8099 by ...sketch...\n-0000d680: 2061 6e64 206e 6f74 2070 6173 7365 640a and not passed.\n-0000d690: 6f6e 2074 6f20 e280 9850 5354 7269 636b on to ...PSTrick\n-0000d6a0: 73e2 8099 2e20 2054 6865 7365 2061 7265 s.... These are\n-0000d6b0: 2073 756d 6d61 7269 7a65 6420 696e 2074 summarized in t\n-0000d6c0: 6865 2066 6f6c 6c6f 7769 6e67 2074 6162 he following tab\n-0000d6d0: 6c65 2e0a 4b65 7920 2020 2020 2020 506f le..Key Po\n-0000d6e0: 7373 6962 6c65 2076 616c 7565 7320 2020 ssible values \n-0000d6f0: 2020 2020 2020 4465 7363 7269 7074 696f Descriptio\n-0000d700: 6e0a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d n.--------------\n+0000d640: 2e0a 0a54 6865 7265 2061 7265 2061 6c73 ...There are als\n+0000d650: 6f20 5f69 6e74 6572 6e61 6c5f 206f 7074 o _internal_ opt\n+0000d660: 696f 6e73 2075 7365 6420 6f6e 6c79 2062 ions used only b\n+0000d670: 7920 e280 9873 6b65 7463 68e2 8099 2061 y ...sketch... a\n+0000d680: 6e64 206e 6f74 2070 6173 7365 640a 6f6e nd not passed.on\n+0000d690: 2074 6f20 e280 9850 5354 7269 636b 73e2 to ...PSTricks.\n+0000d6a0: 8099 2e20 2054 6865 7365 2061 7265 2073 ... 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T\n+0000d790: 7572 6e20 6375 6c6c 696e 6720 6f66 2062 urn culling of b\n+0000d7a0: 6163 6b66 6163 6573 206f 6e20 616e 6420 ackfaces on and \n+0000d7b0: 6f66 6620 7265 7370 6563 7469 7665 6c79 off respectively\n+0000d7c0: 2066 6f72 2074 6869 730a 2020 2020 2020 for this. \n 0000d7d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000d7e0: 2020 2020 2020 2020 2020 2020 2020 6f62 ob\n-0000d7f0: 6a65 6374 2e20 2054 6865 2064 6566 6175 ject. The defau\n-0000d800: 6c74 2076 616c 7565 2069 7320 e280 9874 lt value is ...t\n-0000d810: 7275 65e2 8099 2e0a e280 986c 6179 e280 rue........lay..\n-0000d820: 9920 2020 2020 e280 986f 7665 72e2 8099 . ...over...\n-0000d830: 2c20 e280 9869 6ee2 8099 2c20 e280 9875 , ...in..., ...u\n-0000d840: 6e64 6572 e280 9920 2020 466f 7263 6520 nder... 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Any point may\n-0000dc00: 2068 6176 6520 7468 6520 7a2d 636f 6d70 have the z-comp\n-0000dc10: 6f6e 656e 7420 6f6d 6974 7465 643b 2069 onent omitted; i\n-0000dc20: 7420 7769 6c6c 2064 6566 6175 6c74 0a74 t will default.t\n-0000dc30: 6f20 7a3d 302e 0a0a 2a20 4d65 6e75 3a0a o z=0...* Menu:.\n-0000dc40: 0a2a 2044 7261 7761 626c 6573 3a3a 2020 .* Drawables:: \n-0000dc50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000dc60: 2054 6869 6e67 7320 7468 6174 2061 7265 Things that are\n-0000dc70: 2064 7261 776e 2e0a 2a20 4465 6669 6e69 drawn..* Defini\n-0000dc80: 7469 6f6e 733a 3a20 2020 2020 2020 2020 tions:: \n-0000dc90: 2020 2020 2020 2020 5468 696e 6773 2077 Things w\n-0000dca0: 6974 6820 6e61 6d65 732e 0a0a 1f0a 4669 ith names.....Fi\n-0000dcb0: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-0000dcc0: 2020 4e6f 6465 3a20 4472 6177 6162 6c65 Node: Drawable\n-0000dcd0: 732c 2020 4e65 7874 3a20 4465 6669 6e69 s, Next: Defini\n-0000dce0: 7469 6f6e 732c 2020 5072 6576 3a20 4c61 tions, Prev: La\n-0000dcf0: 6e67 7561 6765 2062 6173 6963 732c 2020 nguage basics, \n-0000dd00: 5570 3a20 496e 7075 7420 6c61 6e67 7561 Up: Input langua\n-0000dd10: 6765 0a0a 332e 3220 4472 6177 6162 6c65 ge..3.2 Drawable\n-0000dd20: 730a 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a s.=============.\n-0000dd30: 0a44 7261 7761 626c 6573 2061 7265 2073 .Drawables are s\n-0000dd40: 696d 706c 7920 e280 9873 6b65 7463 68e2 imply ...sketch.\n-0000dd50: 8099 206f 626a 6563 7473 2074 6861 7420 .. objects that \n-0000dd60: 6d69 6768 7420 6170 7065 6172 2069 6e20 might appear in \n-0000dd70: 7468 6520 6472 6177 696e 672e 0a54 6865 the drawing..The\n-0000dd80: 7920 696e 636c 7564 6520 646f 7473 2c20 y include dots, \n-0000dd90: 706f 6c79 6c69 6e65 732c 2063 7572 7665 polylines, curve\n-0000dda0: 732c 2070 6f6c 7967 6f6e 732c 2061 6e64 s, polygons, and\n-0000ddb0: 206d 6f72 6520 636f 6d70 6c65 7820 6f62 more complex ob\n-0000ddc0: 6a65 6374 730a 7468 6174 2061 7265 2062 jects.that are b\n-0000ddd0: 7569 6c74 2075 7020 6672 6f6d 2073 696d uilt up from sim\n-0000dde0: 706c 6572 206f 6e65 7320 696e 2076 6172 pler ones in var\n-0000ddf0: 696f 7573 2077 6179 732e 2020 4669 6e61 ious ways. 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poly\n-0000def0: 6c69 6e65 732e 0a2a 2043 7572 7665 733a lines..* Curves:\n-0000df00: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0000df10: 2020 2020 2020 2044 7261 7720 6375 7276 Draw curv\n-0000df20: 6573 2e0a 2a20 506f 6c79 676f 6e73 3a3a es..* Polygons::\n+0000dee0: 2020 2020 2044 7261 7720 706f 6c79 6c69 Draw polyli\n+0000def0: 6e65 732e 0a2a 2043 7572 7665 733a 3a20 nes..* Curves:: \n+0000df00: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0000df10: 2020 2020 2044 7261 7720 6375 7276 6573 Draw curves\n+0000df20: 2e0a 2a20 506f 6c79 676f 6e73 3a3a 2020 ..* Polygons:: \n 0000df30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000df40: 2020 2020 4472 6177 2070 6f6c 7967 6f6e Draw polygon\n-0000df50: 732e 0a2a 2053 7065 6369 616c 733a 3a20 s..* Specials:: \n+0000df40: 2020 4472 6177 2070 6f6c 7967 6f6e 732e Draw polygons.\n+0000df50: 0a2a 2053 7065 6369 616c 733a 3a20 2020 .* Specials:: \n 0000df60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000df70: 2020 2045 6d62 6564 2072 6177 204c 6154 Embed raw LaT\n-0000df80: 6558 2061 6e64 20e2 8098 5053 5472 6963 eX and ...PSTric\n-0000df90: 6b73 e280 992e 0a2a 2053 7765 6570 733a ks.....* Sweeps:\n-0000dfa0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0000dfb0: 2020 2020 2020 2044 7261 7720 7377 6565 Draw swee\n-0000dfc0: 7073 206f 6620 646f 7473 2061 6e64 2070 ps of dots and p\n-0000dfd0: 6f6c 796c 696e 6573 2e0a 2a20 426c 6f63 olylines..* Bloc\n-0000dfe0: 6b73 3a3a 2020 2020 2020 2020 2020 2020 ks:: \n-0000dff0: 2020 2020 2020 2020 2020 4772 6f75 7020 Group \n-0000e000: 6f74 6865 7220 6472 6177 6162 6c65 732e other drawables.\n-0000e010: 0a2a 2052 6570 6561 7473 3a3a 2020 2020 .* Repeats:: \n-0000e020: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000e030: 2044 7261 7720 7472 616e 7366 6f72 6d65 Draw transforme\n-0000e040: 6420 636f 7069 6573 206f 6620 6f62 6a65 d copies of obje\n-0000e050: 6374 732e 0a2a 2050 7574 733a 3a20 2020 cts..* Puts:: \n+0000df70: 2045 6d62 6564 2072 6177 204c 6154 6558 Embed raw LaTeX\n+0000df80: 2061 6e64 20e2 8098 5053 5472 6963 6b73 and ...PSTricks\n+0000df90: e280 992e 0a2a 2053 7765 6570 733a 3a20 .....* Sweeps:: \n+0000dfa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0000dfb0: 2020 2020 2044 7261 7720 7377 6565 7073 Draw sweeps\n+0000dfc0: 206f 6620 646f 7473 2061 6e64 2070 6f6c of dots and pol\n+0000dfd0: 796c 696e 6573 2e0a 2a20 426c 6f63 6b73 ylines..* Blocks\n+0000dfe0: 3a3a 2020 2020 2020 2020 2020 2020 2020 :: \n+0000dff0: 2020 2020 2020 2020 4772 6f75 7020 6f74 Group ot\n+0000e000: 6865 7220 6472 6177 6162 6c65 732e 0a2a her drawables..*\n+0000e010: 2052 6570 6561 7473 3a3a 2020 2020 2020 Repeats:: \n+0000e020: 2020 2020 2020 2020 2020 2020 2020 2044 D\n+0000e030: 7261 7720 7472 616e 7366 6f72 6d65 6420 raw transformed \n+0000e040: 636f 7069 6573 206f 6620 6f62 6a65 6374 copies of object\n+0000e050: 732e 0a2a 2050 7574 733a 3a20 2020 2020 s..* Puts:: \n 0000e060: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0000e070: 2020 2020 2044 7261 7720 6f6e 6520 6f62 Draw one ob\n-0000e080: 6a65 6374 2074 7261 6e73 666f 726d 6564 ject transformed\n-0000e090: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n-0000e0a0: 682e 696e 666f 2c20 204e 6f64 653a 2044 h.info, Node: D\n-0000e0b0: 6f74 732c 2020 4e65 7874 3a20 4c69 6e65 ots, Next: Line\n-0000e0c0: 732c 2020 5072 6576 3a20 4472 6177 6162 s, Prev: Drawab\n-0000e0d0: 6c65 732c 2020 5570 3a20 4472 6177 6162 les, Up: Drawab\n-0000e0e0: 6c65 730a 0a33 2e32 2e31 2044 6f74 730a les..3.2.1 Dots.\n-0000e0f0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e ----------..*Syn\n-0000e100: 7461 783a 2a0a 2020 2020 2064 6f74 735b tax:*. dots[\n-0000e110: 4f50 5449 4f4e 535d 2050 4f49 4e54 5f4c OPTIONS] POINT_L\n-0000e120: 4953 540a 5468 6973 2063 6f6d 6d61 6e64 IST.This command\n-0000e130: 2069 7320 7468 6520 7468 7265 652d 6469 is the three-di\n-0000e140: 6d65 6e73 696f 6e61 6c20 6571 7569 7661 mensional equiva\n-0000e150: 6c65 6e74 206f 6620 7468 6520 e280 9850 lent of the ...P\n-0000e160: 5354 7269 636b 73e2 8099 0a63 6f6d 6d61 STricks....comma\n-0000e170: 6e64 20e2 8098 5c70 7364 6f74 73e2 8099 nd ...\\psdots...\n-0000e180: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n-0000e190: 682e 696e 666f 2c20 204e 6f64 653a 204c h.info, Node: L\n-0000e1a0: 696e 6573 2c20 204e 6578 743a 2043 7572 ines, Next: Cur\n-0000e1b0: 7665 732c 2020 5072 6576 3a20 446f 7473 ves, Prev: Dots\n-0000e1c0: 2c20 2055 703a 2044 7261 7761 626c 6573 , Up: Drawables\n-0000e1d0: 0a0a 332e 322e 3220 4c69 6e65 730a 2d2d ..3.2.2 Lines.--\n-0000e1e0: 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 ---------..*Synt\n-0000e1f0: 6178 3a2a 0a20 2020 2020 6c69 6e65 5b4f ax:*. line[O\n-0000e200: 5054 494f 4e53 5d20 504f 494e 545f 4c49 PTIONS] POINT_LI\n-0000e210: 5354 0a54 6869 7320 636f 6d6d 616e 6420 ST.This command \n-0000e220: 6973 2074 6865 2074 6872 6565 2d64 696d is the three-dim\n-0000e230: 656e 7369 6f6e 616c 2065 7175 6976 616c ensional equival\n-0000e240: 656e 7420 6f66 2074 6865 20e2 8098 5053 ent of the ...PS\n-0000e250: 5472 6963 6b73 e280 990a 636f 6d6d 616e Tricks....comman\n-0000e260: 6420 e280 985c 7073 6c69 6e65 e280 992e d ...\\psline....\n-0000e270: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-0000e280: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4375 .info, Node: Cu\n-0000e290: 7276 6573 2c20 204e 6578 743a 2050 6f6c rves, Next: Pol\n-0000e2a0: 7967 6f6e 732c 2020 5072 6576 3a20 4c69 ygons, Prev: Li\n-0000e2b0: 6e65 732c 2020 5570 3a20 4472 6177 6162 nes, Up: Drawab\n-0000e2c0: 6c65 730a 0a33 2e32 2e33 2043 7572 7665 les..3.2.3 Curve\n-0000e2d0: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a s.------------..\n-0000e2e0: 2a53 796e 7461 783a 2a0a 2020 2020 2063 *Syntax:*. c\n-0000e2f0: 7572 7665 5b4f 5054 494f 4e53 5d20 504f urve[OPTIONS] PO\n-0000e300: 494e 545f 4c49 5354 0a54 6869 7320 636f INT_LIST.This co\n-0000e310: 6d6d 616e 6420 6973 2074 6865 2074 6872 mmand is the thr\n-0000e320: 6565 2d64 696d 656e 7369 6f6e 616c 2065 ee-dimensional e\n-0000e330: 7175 6976 616c 656e 7420 6f66 2074 6865 quivalent of the\n-0000e340: 20e2 8098 5053 5472 6963 6b73 e280 990a ...PSTricks....\n-0000e350: 636f 6d6d 616e 6420 e280 985c 7073 6375 command ...\\pscu\n-0000e360: 7276 65e2 8099 2e20 2049 7420 6973 206e rve.... It is n\n-0000e370: 6f74 2069 6d70 6c65 6d65 6e74 6564 2069 ot implemented i\n-0000e380: 6e20 7468 6520 6375 7272 656e 7420 7665 n the current ve\n-0000e390: 7273 696f 6e20 6f66 0ae2 8098 736b 6574 rsion of....sket\n-0000e3a0: 6368 e280 992e 0a0a 1f0a 4669 6c65 3a20 ch........File: \n-0000e3b0: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n-0000e3c0: 6465 3a20 506f 6c79 676f 6e73 2c20 204e de: Polygons, N\n-0000e3d0: 6578 743a 2053 7065 6369 616c 732c 2020 ext: Specials, \n-0000e3e0: 5072 6576 3a20 4375 7276 6573 2c20 2055 Prev: Curves, U\n-0000e3f0: 703a 2044 7261 7761 626c 6573 0a0a 332e p: Drawables..3.\n-0000e400: 322e 3420 506f 6c79 676f 6e73 0a2d 2d2d 2.4 Polygons.---\n-0000e410: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 -----------..*Sy\n-0000e420: 6e74 6178 3a2a 0a20 2020 2020 706f 6c79 ntax:*. poly\n-0000e430: 676f 6e5b 4f50 5449 4f4e 535d 2050 4f49 gon[OPTIONS] POI\n-0000e440: 4e54 5f4c 4953 540a 5468 6973 2063 6f6d NT_LIST.This com\n-0000e450: 6d61 6e64 2069 7320 7468 6520 7468 7265 mand is the thre\n-0000e460: 652d 6469 6d65 6e73 696f 6e61 6c20 6571 e-dimensional eq\n-0000e470: 7569 7661 6c65 6e74 206f 6620 7468 6520 uivalent of the \n-0000e480: e280 9850 5354 7269 636b 73e2 8099 0a63 ...PSTricks....c\n-0000e490: 6f6d 6d61 6e64 20e2 8098 5c70 7370 6f6c ommand ...\\pspol\n-0000e4a0: 7967 6f6e e280 992e 2020 5468 6520 e280 ygon.... The ..\n-0000e4b0: 9873 6b65 7463 68e2 8099 2068 6964 6465 .sketch... hidde\n-0000e4c0: 6e20 7375 7266 6163 6520 616c 676f 7269 n surface algori\n-0000e4d0: 7468 6d20 6173 7375 6d65 730a 7468 6174 thm assumes.that\n-0000e4e0: 2070 6f6c 7967 6f6e 7320 6172 6520 636f polygons are co\n-0000e4f0: 6e76 6578 2061 6e64 2070 6c61 6e61 722e nvex and planar.\n-0000e500: 2020 496e 2070 7261 6374 6963 652c 2064 In practice, d\n-0000e510: 7261 7769 6e67 7320 6d61 7920 7765 6c6c rawings may well\n-0000e520: 0a74 7572 6e20 6f75 7420 636f 7272 6563 .turn out correc\n-0000e530: 746c 7920 6576 656e 2069 6620 7468 6573 tly even if thes\n-0000e540: 6520 6173 7375 6d70 7469 6f6e 7320 6172 e assumptions ar\n-0000e550: 6520 7669 6f6c 6174 6564 2e0a 0a1f 0a46 e violated.....F\n-0000e560: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-0000e570: 2c20 204e 6f64 653a 2053 7065 6369 616c , Node: Special\n-0000e580: 732c 2020 4e65 7874 3a20 5377 6565 7073 s, Next: Sweeps\n-0000e590: 2c20 2050 7265 763a 2050 6f6c 7967 6f6e , Prev: Polygon\n-0000e5a0: 732c 2020 5570 3a20 4472 6177 6162 6c65 s, Up: Drawable\n-0000e5b0: 730a 0a33 2e32 2e35 2053 7065 6369 616c s..3.2.5 Special\n-0000e5c0: 730a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d s.--------------\n-0000e5d0: 0a0a 2a53 796e 7461 783a 2a0a 2020 2020 ..*Syntax:*. \n-0000e5e0: 2073 7065 6369 616c 2024 5241 575f 5445 special $RAW_TE\n-0000e5f0: 5854 245b 4f50 5449 4f4e 535d 2041 5247 XT$[OPTIONS] ARG\n-0000e600: 5f4c 4953 540a 4865 7265 20e2 8098 24e2 _LIST.Here ...$.\n-0000e610: 8099 2063 616e 2062 6520 616e 7920 6368 .. can be any ch\n-0000e620: 6172 6163 7465 7220 616e 6420 6973 2075 aracter and is u\n-0000e630: 7365 6420 746f 2064 656c 696d 6974 2074 sed to delimit t\n-0000e640: 6865 2073 7461 7274 2061 6e64 2065 6e64 he start and end\n-0000e650: 0a6f 6620 5241 575f 5445 5854 2e20 2054 .of RAW_TEXT. T\n-0000e660: 6865 2063 6f6d 6d61 6e64 2065 6d62 6564 he command embed\n-0000e670: 7320 5241 575f 5445 5854 2069 6e20 7468 s RAW_TEXT in th\n-0000e680: 6520 e280 9873 6b65 7463 68e2 8099 206f e ...sketch... o\n-0000e690: 7574 7075 7420 6166 7465 720a 7065 7266 utput after.perf\n-0000e6a0: 6f72 6d69 6e67 2073 7562 7374 6974 7574 orming substitut\n-0000e6b0: 696f 6e73 2061 7320 666f 6c6c 6f77 732e ions as follows.\n-0000e6c0: 0a20 2020 e280 a220 e280 9823 49e2 8099 . ... ...#I...\n-0000e6d0: 2077 6865 7265 2049 2069 7320 6120 706f where I is a po\n-0000e6e0: 7369 7469 7665 2069 6e74 6567 6572 2069 sitive integer i\n-0000e6f0: 7320 7265 706c 6163 6564 2062 7920 7468 s replaced by th\n-0000e700: 6520 4927 7468 2076 616c 7565 2069 6e0a e I'th value in.\n-0000e710: 2020 2020 2041 5247 5f4c 4953 542e 2020 ARG_LIST. \n-0000e720: 506f 696e 7420 616e 6420 7665 6374 6f72 Point and vector\n-0000e730: 2061 7267 756d 656e 7473 2062 6563 6f6d arguments becom\n-0000e740: 6520 7477 6f2d 6469 6d65 6e73 696f 6e61 e two-dimensiona\n-0000e750: 6c0a 2020 2020 2070 6f69 6e74 732c 2077 l. points, w\n-0000e760: 6869 6368 2061 7265 2074 6865 2074 7261 hich are the tra\n-0000e770: 6e73 666f 726d 6564 2033 6420 6172 6775 nsformed 3d argu\n-0000e780: 6d65 6e74 7320 7072 6f6a 6563 7465 6420 ments projected \n-0000e790: 6f6e 746f 2074 6865 0a20 2020 2020 582d onto the. X-\n-0000e7a0: 5920 706c 616e 652e 2020 5468 6973 2061 Y plane. This a\n-0000e7b0: 6c6c 6f77 7320 7477 6f2d 6469 6d65 6e74 llows two-diment\n-0000e7c0: 696f 6e61 6c20 6f75 7470 7574 2065 6c65 ional output ele\n-0000e7d0: 6d65 6e74 7320 7375 6368 2061 730a 2020 ments such as. \n-0000e7e0: 2020 206c 6162 656c 7320 746f 2062 6520 labels to be \n-0000e7f0: 6561 7369 6c79 2070 6f73 6974 696f 6e65 easily positione\n-0000e800: 6420 7769 7468 2072 6573 7065 6374 2074 d with respect t\n-0000e810: 6f20 7468 7265 652d 6469 6d65 6e73 696f o three-dimensio\n-0000e820: 6e61 6c0a 2020 2020 2066 6561 7475 7265 nal. feature\n-0000e830: 7320 696e 2074 6865 2064 7261 7769 6e67 s in the drawing\n-0000e840: 2e20 2053 6361 6c61 7220 6172 6775 6d65 . Scalar argume\n-0000e850: 6e74 7320 6172 6520 7375 6273 6974 7574 nts are subsitut\n-0000e860: 6564 2064 6972 6563 746c 792e 0a20 2020 ed directly.. \n-0000e870: 2020 4e6f 2074 7261 6e73 666f 726d 6174 No transformat\n-0000e880: 696f 6e20 6973 2061 7070 6c69 6564 2e0a ion is applied..\n-0000e890: 2020 20e2 80a2 20e2 8098 237b 497d e280 ... ...#{I}..\n-0000e8a0: 9920 6973 2061 6c73 6f20 7265 706c 6163 . is also replac\n-0000e8b0: 6564 2061 7320 6162 6f76 652e 0a20 2020 ed as above.. \n-0000e8c0: e280 a220 e280 9823 4927 32e2 8099 2069 ... ...#I'2... i\n-0000e8d0: 7320 7265 706c 6163 6564 2061 7320 6162 s replaced as ab\n-0000e8e0: 6f76 6520 666f 7220 706f 696e 7473 206f ove for points o\n-0000e8f0: 7220 7665 6374 6f72 732e 2020 4974 2069 r vectors. It i\n-0000e900: 7320 616e 2065 7272 6f72 0a20 2020 2020 s an error. \n-0000e910: 666f 7220 7468 6520 4927 7468 2061 7267 for the I'th arg\n-0000e920: 756d 656e 7420 746f 2062 6520 6120 7363 ument to be a sc\n-0000e930: 616c 6172 2e0a 2020 20e2 80a2 20e2 8098 alar.. ... ...\n-0000e940: 2349 2778 e280 992c 20e2 8098 2349 2779 #I'x..., ...#I'y\n-0000e950: e280 992c 206f 7220 e280 9823 4927 7ae2 ..., or ...#I'z.\n-0000e960: 8099 2069 7320 7265 706c 6163 6564 2c20 .. is replaced, \n-0000e970: 7265 7370 6563 7469 7665 6c79 2c20 6279 respectively, by\n-0000e980: 2074 6865 2073 6361 6c61 720a 2020 2020 the scalar. \n-0000e990: 2058 2c20 592c 206f 7220 5a2d 636f 6f72 X, Y, or Z-coor\n-0000e9a0: 6469 6e61 7465 206f 6620 7468 6520 6172 dinate of the ar\n-0000e9b0: 6775 6d65 6e74 2070 6f69 6e74 206f 7220 gument point or \n-0000e9c0: 7665 6374 6f72 2e20 2049 7420 6973 2061 vector. It is a\n-0000e9d0: 6e0a 2020 2020 2065 7272 6f72 2066 6f72 n. error for\n-0000e9e0: 2074 6865 2049 2774 6820 6172 6775 6d65 the I'th argume\n-0000e9f0: 6e74 2074 6f20 6265 2061 2073 6361 6c61 nt to be a scala\n-0000ea00: 722e 0a20 2020 e280 a220 e280 9823 4927 r.. ... ...#I'\n-0000ea10: 33e2 8099 2069 7320 7265 706c 6163 6564 3... is replaced\n-0000ea20: 2062 7920 7468 6520 7468 7265 652d 6469 by the three-di\n-0000ea30: 6d65 6e73 696f 6e61 6c20 7472 616e 7366 mensional transf\n-0000ea40: 6f72 6d65 6420 6172 6775 6d65 6e74 2e0a ormed argument..\n-0000ea50: 2020 2020 204e 6f74 6520 7468 6174 2069 Note that i\n-0000ea60: 6620 6120 7065 7273 7065 6374 6976 6520 f a perspective \n-0000ea70: 7472 616e 7366 6f72 6d61 7469 6f6e 2068 transformation h\n-0000ea80: 6173 2062 6565 6e20 6170 706c 6965 642c as been applied,\n-0000ea90: 2074 6865 0a20 2020 2020 5a2d 636f 6f72 the. Z-coor\n-0000eaa0: 6469 6e61 7465 2068 6173 206c 6974 746c dinate has littl\n-0000eab0: 6520 6765 6f6d 6574 7269 6320 7369 676e e geometric sign\n-0000eac0: 6966 6963 616e 6365 2c20 7468 6f75 6768 ificance, though\n-0000ead0: 2069 740a 2020 2020 2061 6363 7572 6174 it. accurat\n-0000eae0: 656c 7920 696e 6469 6361 7465 7320 7265 ely indicates re\n-0000eaf0: 6c61 7469 7665 2064 6570 7468 2e0a 2020 lative depth.. \n-0000eb00: 20e2 80a2 20e2 8098 2349 2d4a e280 9920 ... ...#I-J... \n-0000eb10: 7768 6572 6520 4920 616e 6420 4a20 6172 where I and J ar\n-0000eb20: 6520 706f 7369 7469 7665 2069 6e74 6567 e positive integ\n-0000eb30: 6572 7320 6973 2072 6570 6c61 6365 6420 ers is replaced \n-0000eb40: 6279 2061 2073 7472 696e 670a 2020 2020 by a string. \n-0000eb50: 20e2 8098 7b41 4e47 4c45 7de2 8099 2077 ...{ANGLE}... w\n-0000eb60: 6865 7265 2041 4e47 4c45 2069 7320 7468 here ANGLE is th\n-0000eb70: 6520 706f 6c61 7220 616e 676c 6520 6f66 e polar angle of\n-0000eb80: 2061 2076 6563 746f 7220 6672 6f6d 2074 a vector from t\n-0000eb90: 6865 2049 2774 680a 2020 2020 2070 6f69 he I'th. poi\n-0000eba0: 6e74 2069 6e20 504f 494e 545f 4c49 5354 nt in POINT_LIST\n-0000ebb0: 2074 6f20 7468 6520 4a27 7468 2070 6f69 to the J'th poi\n-0000ebc0: 6e74 2070 726f 6a65 6374 6564 2069 6e74 nt projected int\n-0000ebd0: 6f20 7468 6520 782d 7920 706c 616e 652e o the x-y plane.\n-0000ebe0: 0a20 2020 2020 4974 2069 7320 616e 2065 . It is an e\n-0000ebf0: 7272 6f72 2066 6f72 2074 6865 2049 2774 rror for the I't\n-0000ec00: 6820 6f72 204a 2774 6820 6172 6775 6d65 h or J'th argume\n-0000ec10: 6e74 2074 6f20 6265 2061 2073 6361 6c61 nt to be a scala\n-0000ec20: 7220 6f72 2061 0a20 2020 2020 7665 6374 r or a. vect\n-0000ec30: 6f72 2e0a 2020 20e2 80a2 20e2 8098 237b or.. ... ...#{\n-0000ec40: 492d 4a7d e280 9920 6973 2061 6c73 6f20 I-J}... is also \n-0000ec50: 7265 706c 6163 6564 2061 7320 6162 6f76 replaced as abov\n-0000ec60: 652e 0a20 2020 e280 a220 e280 9823 23e2 e.. ... ...##.\n-0000ec70: 8099 2069 7320 7265 706c 6163 6564 2077 .. is replaced w\n-0000ec80: 6974 6820 e280 9823 e280 992e 0a54 6865 ith ...#.....The\n-0000ec90: 2066 6f72 6d73 2077 6974 6820 6272 6163 forms with brac\n-0000eca0: 6573 20e2 8098 7b20 7de2 8099 2061 7265 es ...{ }... are\n-0000ecb0: 2075 7365 6675 6c20 7768 656e 2074 6865 useful when the\n-0000ecc0: 2061 7267 756d 656e 7420 6973 2069 6d6d argument is imm\n-0000ecd0: 6564 6961 7465 6c79 0a66 6f6c 6c6f 7765 ediately.followe\n-0000ece0: 6420 6279 2061 2064 6967 6974 206f 7220 d by a digit or \n-0000ecf0: 6120 7469 636b 2063 6861 7261 6374 6572 a tick character\n-0000ed00: 2074 6861 7420 6973 2070 6172 7420 6f66 that is part of\n-0000ed10: 2074 6865 2054 6558 2063 6f64 652e 0a0a the TeX code...\n-0000ed20: 2020 2054 6865 206f 6e6c 7920 7573 6566 The only usef\n-0000ed30: 756c 206f 7074 696f 6e20 6f66 20e2 8098 ul option of ...\n-0000ed40: 7370 6563 6961 6ce2 8099 2069 7320 e280 special... is ..\n-0000ed50: 986c 6179 e280 992c 2077 6869 6368 2064 .lay..., which d\n-0000ed60: 6574 6572 6d69 6e65 7320 6966 2074 6865 etermines if the\n-0000ed70: 0a73 7562 7374 6974 7565 6420 7261 7720 .substitued raw \n-0000ed80: 7465 7874 2069 7320 656d 6974 7465 6420 text is emitted \n-0000ed90: 6265 666f 7265 2c20 6166 7465 722c 206f before, after, o\n-0000eda0: 7220 7573 696e 6720 7468 6520 6669 7273 r using the firs\n-0000edb0: 7420 706f 696e 740a 696e 2050 4f49 4e54 t point.in POINT\n-0000edc0: 5f4c 4953 5420 6173 2061 6e20 696e 6469 _LIST as an indi\n-0000edd0: 6361 746f 7220 6f66 2064 6570 7468 2e20 cator of depth. \n-0000ede0: 2054 6865 7365 206f 6363 7572 2c20 7265 These occur, re\n-0000edf0: 7370 6563 7469 7665 6c79 2c20 7769 7468 spectively, with\n-0000ee00: 0ae2 8098 6c61 793d 756e 6465 72e2 8099 ....lay=under...\n-0000ee10: 2c20 e280 986c 6179 3d6f 7665 72e2 8099 , ...lay=over...\n-0000ee20: 2c20 616e 6420 e280 986c 6179 3d69 6ee2 , and ...lay=in.\n-0000ee30: 8099 2e20 2053 6565 202a 6e6f 7465 2053 ... See *note S\n-0000ee40: 7065 6369 616c 206f 626a 6563 7473 3a3a pecial objects::\n-0000ee50: 2061 6e64 0a2a 6e6f 7465 2054 696b 5a2f and.*note TikZ/\n-0000ee60: 5047 4620 7573 6572 2d64 6566 696e 6564 PGF user-defined\n-0000ee70: 2073 7479 6c65 733a 3a20 666f 7220 6578 styles:: for ex\n-0000ee80: 616d 706c 6573 2e20 202a 4e6f 7465 2049 amples. *Note I\n-0000ee90: 6e74 6572 6e61 6c0a 6f70 7469 6f6e 733a nternal.options:\n-0000eea0: 3a2e 0a0a 1f0a 4669 6c65 3a20 736b 6574 :.....File: sket\n-0000eeb0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-0000eec0: 5377 6565 7073 2c20 204e 6578 743a 2042 Sweeps, Next: B\n-0000eed0: 6c6f 636b 732c 2020 5072 6576 3a20 5370 locks, Prev: Sp\n-0000eee0: 6563 6961 6c73 2c20 2055 703a 2044 7261 ecials, Up: Dra\n-0000eef0: 7761 626c 6573 0a0a 332e 322e 3620 5377 wables..3.2.6 Sw\n-0000ef00: 6565 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d eeps.-----------\n-0000ef10: 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 2020 -..*Syntax:*. \n-0000ef20: 2020 7377 6565 7020 7b20 4e2c 2054 5f31 sweep { N, T_1\n-0000ef30: 2c20 545f 322c 202e 2e2e 2c20 545f 5220 , T_2, ..., T_R \n-0000ef40: 7d5b 4f50 5449 4f4e 535d 2053 5745 5054 }[OPTIONS] SWEPT\n-0000ef50: 5f4f 424a 4543 540a 2020 2020 2073 7765 _OBJECT. swe\n-0000ef60: 6570 207b 204e 3c3e 2c20 545f 312c 2054 ep { N<>, T_1, T\n-0000ef70: 5f32 2c20 2e2e 2e2c 2054 5f52 207d 5b4f _2, ..., T_R }[O\n-0000ef80: 5054 494f 4e53 5d20 5357 4550 545f 4f42 PTIONS] SWEPT_OB\n-0000ef90: 4a45 4354 0a54 6865 2073 7765 6570 2063 JECT.The sweep c\n-0000efa0: 6f6e 6e65 6374 7320 4e20 286f 7220 7065 onnects N (or pe\n-0000efb0: 7268 6170 7320 4e2b 3129 2063 6f70 6965 rhaps N+1) copie\n-0000efc0: 7320 6f66 2053 5745 5054 5f4f 424a 4543 s of SWEPT_OBJEC\n-0000efd0: 5420 696e 206f 7264 6572 2074 6f0a 6372 T in order to.cr\n-0000efe0: 6561 7465 2061 206e 6577 206f 626a 6563 eate a new objec\n-0000eff0: 7420 6f66 2068 6967 6865 7220 6469 6d65 t of higher dime\n-0000f000: 6e73 696f 6e2e 2020 5468 6520 545f 4920 nsion. The T_I \n-0000f010: 2866 6f72 2069 2062 6574 7765 656e 2031 (for i between 1\n-0000f020: 2061 6e64 0a72 2920 6172 6520 7472 616e and.r) are tran\n-0000f030: 7366 6f72 6d73 2e20 2054 6865 206b 2774 sforms. The k't\n-0000f040: 6820 636f 7079 206f 6620 5357 4550 545f h copy of SWEPT_\n-0000f050: 4f42 4a45 4354 2069 7320 7072 6f64 7563 OBJECT is produc\n-0000f060: 6564 2062 790a 6170 706c 7969 6e67 2074 ed by.applying t\n-0000f070: 6865 2066 6f6c 6c6f 7769 6e67 2074 7261 he following tra\n-0000f080: 6e73 666f 726d 2074 6f20 7468 6520 6f72 nsform to the or\n-0000f090: 6967 696e 616c 2e0a 2020 2020 2054 5f31 iginal.. T_1\n-0000f0a0: 5e6b 2074 6865 6e20 545f 325e 6b20 7468 ^k then T_2^k th\n-0000f0b0: 656e 202e 2e2e 2074 6865 6e20 545f 525e en ... then T_R^\n-0000f0c0: 6b0a 4865 7265 2054 5e6b 206d 6561 6e73 k.Here T^k means\n-0000f0d0: 2022 7472 616e 7366 6f72 6d20 5420 6170 \"transform T ap\n-0000f0e0: 706c 6965 6420 6b20 7469 6d65 732e 2220 plied k times.\" \n-0000f0f0: 2054 6865 206f 7269 6769 6e61 6c20 6f62 The original ob\n-0000f100: 6a65 6374 2069 730a 7468 6520 7a65 726f ject is.the zero\n-0000f110: 2774 6820 636f 7079 2c20 7769 7468 206b 'th copy, with k\n-0000f120: 3d30 2061 6e64 2065 6666 6563 7469 7665 =0 and effective\n-0000f130: 6c79 206e 6f20 7472 616e 7366 6f72 6d20 ly no transform \n-0000f140: 6170 706c 6965 6420 2854 5e30 3d49 2c0a applied (T^0=I,.\n-0000f150: 7468 6520 6964 656e 7469 7479 2074 7261 the identity tra\n-0000f160: 6e73 666f 726d 292e 0a0a 2020 2054 6865 nsform)... The\n-0000f170: 206d 6574 686f 6420 6f66 2063 6f6e 6e65 method of conne\n-0000f180: 6374 696e 6720 7468 6520 636f 7069 6573 cting the copies\n-0000f190: 2064 6570 656e 6473 206f 6e20 7468 6520 depends on the \n-0000f1a0: 7479 7065 206f 660a 5357 4550 545f 4f42 type of.SWEPT_OB\n-0000f1b0: 4a45 4354 2061 6e64 206f 6e20 7768 6574 JECT and on whet\n-0000f1c0: 6865 7220 7468 6520 636c 6f73 7572 6520 her the closure \n-0000f1d0: 7461 6720 e280 983c 3ee2 8099 2069 7320 tag ...<>... is \n-0000f1e0: 7072 6573 656e 7420 6f72 206e 6f74 2e0a present or not..\n-0000f1f0: 0a20 2020 416e 2065 7861 6d70 6c65 206f . An example o\n-0000f200: 6620 6120 7377 6565 7020 7768 6572 6520 f a sweep where \n-0000f210: 723d 3220 6973 2074 6865 204d 6f62 6975 r=2 is the Mobiu\n-0000f220: 7320 6669 6775 7265 2061 7420 2a6e 6f74 s figure at *not\n-0000f230: 6520 4d6f 7265 2074 6f0a 6c65 6172 6e3a e More to.learn:\n-0000f240: 3a2e 0a0a 2a20 4d65 6e75 3a0a 0a2a 2053 :...* Menu:..* S\n-0000f250: 7765 7074 2070 6f69 6e74 733a 3a20 2020 wept points:: \n-0000f260: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-0000f270: 7074 2070 6f69 6e74 7320 6d61 6b65 206c pt points make l\n-0000f280: 696e 6573 206f 7220 706f 6c79 676f 6e73 ines or polygons\n-0000f290: 2e0a 2a20 5377 6570 7420 6c69 6e65 733a ..* Swept lines:\n-0000f2a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0000f2b0: 2020 5377 6570 7420 6c69 6e65 7320 6d61 Swept lines ma\n-0000f2c0: 6b65 206f 7065 6e20 6f72 2063 6c6f 7365 ke open or close\n-0000f2d0: 6420 7375 7266 6163 6573 2e0a 2a20 5377 d surfaces..* Sw\n-0000f2e0: 6570 7420 706f 6c79 676f 6e73 3a3a 2020 ept polygons:: \n-0000f2f0: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n-0000f300: 7420 706f 6c79 676f 6e73 206d 616b 6520 t polygons make \n-0000f310: 636c 6f73 6564 2073 7572 6661 6365 732e closed surfaces.\n-0000f320: 0a2a 2053 7765 7074 2062 6c6f 636b 733a .* Swept blocks:\n-0000f330: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0000f340: 2053 7765 7074 2062 6c6f 636b 20e2 89a1 Swept block ...\n-0000f350: 2062 6c6f 636b 206f 6620 7377 6565 7073 block of sweeps\n-0000f360: 2e0a 2a20 5377 6565 7020 6661 6365 2073 ..* Sweep face s\n-0000f370: 706c 6974 7469 6e67 3a3a 2020 2020 2020 plitting:: \n-0000f380: 2020 4669 7869 6e67 2077 6172 7065 6420 Fixing warped \n-0000f390: 6661 6365 7320 7769 7468 2074 7269 616e faces with trian\n-0000f3a0: 676c 6573 2e0a 0a1f 0a46 696c 653a 2073 gles.....File: s\n-0000f3b0: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n-0000f3c0: 653a 2053 7765 7074 2070 6f69 6e74 732c e: Swept points,\n-0000f3d0: 2020 4e65 7874 3a20 5377 6570 7420 6c69 Next: Swept li\n-0000f3e0: 6e65 732c 2020 5072 6576 3a20 5377 6565 nes, Prev: Swee\n-0000f3f0: 7073 2c20 2055 703a 2053 7765 6570 730a ps, Up: Sweeps.\n-0000f400: 0a33 2e32 2e36 2e31 2053 7765 7074 2070 .3.2.6.1 Swept p\n-0000f410: 6f69 6e74 730a 2e2e 2e2e 2e2e 2e2e 2e2e oints...........\n-0000f420: 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 4966 2053 ............If S\n-0000f430: 5745 5054 5f4f 424a 4543 5420 6973 2061 WEPT_OBJECT is a\n-0000f440: 2070 6f69 6e74 206c 6973 7420 616e 6420 point list and \n-0000f450: 7468 6572 6520 6973 206e 6f20 636c 6f73 there is no clos\n-0000f460: 7572 6520 7461 672c 2074 6865 6e0a e280 ure tag, then...\n-0000f470: 9873 7765 6570 e280 9920 636f 6e6e 6563 .sweep... connec\n-0000f480: 7473 204e 2b31 2073 7563 6365 7373 6976 ts N+1 successiv\n-0000f490: 6520 636f 7069 6573 206f 6620 6561 6368 e copies of each\n-0000f4a0: 2070 6f69 6e74 2028 696e 636c 7564 696e point (includin\n-0000f4b0: 6720 7468 650a 6f72 6967 696e 616c 2920 g the.original) \n-0000f4c0: 7769 7468 2073 7472 6169 6768 7420 6c69 with straight li\n-0000f4d0: 6e65 2073 6567 6d65 6e74 7320 746f 2066 ne segments to f\n-0000f4e0: 6f72 6d20 6120 706f 6c79 6c69 6e65 2e20 orm a polyline. \n-0000f4f0: 2049 6620 7468 6572 6520 6172 650a 6d20 If there are.m \n-0000f500: 706f 696e 7473 2069 6e20 7468 6520 6f72 points in the or\n-0000f510: 6967 696e 616c 2070 6f69 6e74 206c 6973 iginal point lis\n-0000f520: 742c 2074 6865 6e20 6d20 706f 6c79 6c69 t, then m polyli\n-0000f530: 6e65 7320 7769 7468 204e 2073 6567 6d65 nes with N segme\n-0000f540: 6e74 730a 6561 6368 2061 7265 2066 6f72 nts.each are for\n-0000f550: 6d65 6420 6279 2074 6865 2073 7765 6570 med by the sweep\n-0000f560: 2e20 2049 6e20 7468 6973 206d 616e 6e65 . In this manne\n-0000f570: 722c 20e2 8098 7377 6565 70e2 8099 2066 r, ...sweep... f\n-0000f580: 6f72 6d73 2061 2073 6574 206f 660a 6f6e orms a set of.on\n-0000f590: 652d 6469 6d65 6e73 696f 6e61 6c20 6f62 e-dimensional ob\n-0000f5a0: 6a65 6374 7320 2870 6f6c 796c 696e 6573 jects (polylines\n-0000f5b0: 2920 6672 6f6d 207a 6572 6f2d 6469 6d65 ) from zero-dime\n-0000f5c0: 6e73 696f 6e61 6c20 6f6e 6573 2028 706f nsional ones (po\n-0000f5d0: 696e 7473 292e 0a0a 2020 2057 6865 6e20 ints)... When \n-0000f5e0: 7468 6572 6520 5f69 735f 2061 2063 6c6f there _is_ a clo\n-0000f5f0: 7375 7265 2074 6167 2c20 e280 9873 7765 sure tag, ...swe\n-0000f600: 6570 e280 9920 636f 6e6e 6563 7473 204e ep... connects N\n-0000f610: 2073 7563 6365 7373 6976 6520 636f 7069 successive copi\n-0000f620: 6573 0a6f 6620 6561 6368 2070 6f69 6e74 es.of each point\n-0000f630: 2028 696e 636c 7564 696e 6720 7468 6520 (including the \n-0000f640: 6f72 6967 696e 616c 2920 7769 7468 2073 original) with s\n-0000f650: 7472 6169 6768 7420 6c69 6e65 2073 6567 traight line seg\n-0000f660: 6d65 6e74 7320 616e 640a 6669 6e61 6c6c ments and.finall\n-0000f670: 7920 636f 6e6e 6563 7473 2074 6865 206c y connects the l\n-0000f680: 6173 7420 636f 7079 2062 6163 6b20 746f ast copy back to\n-0000f690: 2074 6865 206f 7269 6769 6e61 6c20 746f the original to\n-0000f6a0: 2066 6f72 6d20 6120 706f 6c79 676f 6e0a form a polygon.\n-0000f6b0: 7769 7468 204e 2073 6964 6573 2e20 2049 with N sides. I\n-0000f6c0: 6620 7468 6572 6520 6172 6520 6d20 706f f there are m po\n-0000f6d0: 696e 7473 2069 6e20 7468 6520 6f72 6967 ints in the orig\n-0000f6e0: 696e 616c 2070 6f69 6e74 206c 6973 742c inal point list,\n-0000f6f0: 2074 6865 6e20 6d0a 706f 6c79 676f 6e73 then m.polygons\n-0000f700: 2077 6974 6820 4e20 7369 6465 7320 6561 with N sides ea\n-0000f710: 6368 2061 7265 2066 6f72 6d65 6420 6279 ch are formed by\n-0000f720: 2074 6865 2073 7765 6570 2e20 2049 6e20 the sweep. In \n-0000f730: 7468 6973 206d 616e 6e65 722c 0ae2 8098 this manner,....\n-0000f740: 7377 6565 70e2 8099 2066 6f72 6d73 2061 sweep... forms a\n-0000f750: 2073 6574 206f 6620 7477 6f2d 6469 6d65 set of two-dime\n-0000f760: 6e73 696f 6e61 6c20 6f62 6a65 6374 7320 nsional objects \n-0000f770: 2870 6f6c 7967 6f6e 7329 2066 726f 6d0a (polygons) from.\n-0000f780: 7a65 726f 2d64 696d 656e 7369 6f6e 616c zero-dimensional\n-0000f790: 206f 6e65 7320 2870 6f69 6e74 7329 2e0a ones (points)..\n-0000f7a0: 0a20 2020 4f70 7469 6f6e 7320 6f66 2074 . Options of t\n-0000f7b0: 6865 20e2 8098 7377 6565 70e2 8099 2061 he ...sweep... a\n-0000f7c0: 7265 2063 6f70 6965 6420 6469 7265 6374 re copied direct\n-0000f7d0: 6c79 2074 6f20 7468 6520 7265 7375 6c74 ly to the result\n-0000f7e0: 696e 670a 706f 6c79 6c69 6e65 2873 292e ing.polyline(s).\n-0000f7f0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-0000f800: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377 .info, Node: Sw\n-0000f810: 6570 7420 6c69 6e65 732c 2020 4e65 7874 ept lines, Next\n-0000f820: 3a20 5377 6570 7420 706f 6c79 676f 6e73 : Swept polygons\n-0000f830: 2c20 2050 7265 763a 2053 7765 7074 2070 , Prev: Swept p\n-0000f840: 6f69 6e74 732c 2020 5570 3a20 5377 6565 oints, Up: Swee\n-0000f850: 7073 0a0a 332e 322e 362e 3220 5377 6570 ps..3.2.6.2 Swep\n-0000f860: 7420 6c69 6e65 730a 2e2e 2e2e 2e2e 2e2e t lines.........\n-0000f870: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a49 6620 .............If \n-0000f880: 5357 4550 545f 4f42 4a45 4354 2069 7320 SWEPT_OBJECT is \n-0000f890: 6120 706f 6c79 6c69 6e65 2061 6e64 2074 a polyline and t\n-0000f8a0: 6865 7265 2069 7320 6e6f 2063 6c6f 7375 here is no closu\n-0000f8b0: 7265 2074 6167 2c20 7468 656e 20e2 8098 re tag, then ...\n-0000f8c0: 7377 6565 70e2 8099 0a63 6f6e 6e65 6374 sweep....connect\n-0000f8d0: 7320 4e2b 3120 7375 6363 6573 7369 7665 s N+1 successive\n-0000f8e0: 2063 6f70 6965 7320 6f66 2074 6865 2070 copies of the p\n-0000f8f0: 6f6c 796c 696e 6520 2869 6e63 6c75 6469 olyline (includi\n-0000f900: 6e67 2074 6865 206f 7269 6769 6e61 6c29 ng the original)\n-0000f910: 0a77 6974 6820 666f 7572 2d73 6964 6564 .with four-sided\n-0000f920: 2070 6f6c 7967 6f6e 732c 2065 6163 6820 polygons, each \n-0000f930: 7061 6972 206f 6620 636f 7069 6573 2067 pair of copies g\n-0000f940: 6976 696e 6720 7269 7365 2074 6f20 6120 iving rise to a \n-0000f950: 2270 6f6c 7967 6f6e 0a73 7472 6970 2e22 \"polygon.strip.\"\n-0000f960: 2020 4966 2074 6865 7265 2061 7265 206d If there are m\n-0000f970: 2070 6f69 6e74 7320 696e 2074 6865 206f points in the o\n-0000f980: 7269 6769 6e61 6c20 706f 6c79 6c69 6e65 riginal polyline\n-0000f990: 2c20 7468 656e 2028 6d2d 3129 4e0a 706f , then (m-1)N.po\n-0000f9a0: 6c79 676f 6e73 2061 7265 2066 6f72 6d65 lygons are forme\n-0000f9b0: 6420 6279 2074 6865 2073 7765 6570 2e20 d by the sweep. \n-0000f9c0: 2057 6520 6361 6c6c 2074 6865 7365 20e2 We call these .\n-0000f9d0: 809c 626f 6479 2070 6f6c 7967 6f6e 73e2 ..body polygons.\n-0000f9e0: 809d 2e20 2049 6e0a 7468 6973 206d 616e ... In.this man\n-0000f9f0: 6e65 722c 20e2 8098 7377 6565 70e2 8099 ner, ...sweep...\n-0000fa00: 2066 6f72 6d73 2061 2074 776f 2d64 696d forms a two-dim\n-0000fa10: 656e 7369 6f6e 616c 2073 7572 6661 6365 ensional surface\n-0000fa20: 2066 726f 6d20 6672 6f6d 2061 0a6f 6e65 from from a.one\n-0000fa30: 2d64 696d 656e 7369 6f6e 616c 2070 6f6c -dimensional pol\n-0000fa40: 796c 696e 652e 0a0a 2020 2054 6865 206f yline... The o\n-0000fa50: 7264 6572 206f 6620 7665 7274 6963 6573 rder of vertices\n-0000fa60: 2070 726f 6475 6365 6420 6279 20e2 8098 produced by ...\n-0000fa70: 7377 6565 70e2 8099 2069 7320 696d 706f sweep... is impo\n-0000fa80: 7274 616e 742e 2020 4966 2061 0a70 6f6c rtant. If a.pol\n-0000fa90: 7967 6f6e 2773 2076 6572 7469 6365 7320 ygon's vertices \n-0000faa0: 646f 206e 6f74 2061 7070 6561 7220 696e do not appear in\n-0000fab0: 2063 6f75 6e74 6572 2d63 6c6f 636b 7769 counter-clockwi\n-0000fac0: 7365 206f 7264 6572 2069 6e20 7468 6520 se order in the \n-0000fad0: 6669 6e61 6c0a 696d 6167 652c 2074 6865 final.image, the\n-0000fae0: 2070 6f6c 7967 6f6e 2077 696c 6c20 6265 polygon will be\n-0000faf0: 2063 756c 6c65 6420 2875 6e6c 6573 7320 culled (unless \n-0000fb00: e280 9863 756c 6c3d 6661 6c73 65e2 8099 ...cull=false...\n-0000fb10: 2069 7320 7365 7429 2e20 2049 6620 7468 is set). If th\n-0000fb20: 650a 706f 696e 7473 2069 6e20 7468 6520 e.points in the \n-0000fb30: 6b27 7468 2063 6f70 7920 6f66 2074 6865 k'th copy of the\n-0000fb40: 2070 6f6c 796c 696e 6520 6172 6520 505f polyline are P_\n-0000fb50: 312c 2050 5f32 2c20 2e2e 2e2c 2050 5f6d 1, P_2, ..., P_m\n-0000fb60: 2c20 616e 6420 7468 650a 706f 696e 7473 , and the.points\n-0000fb70: 2069 6e20 7468 6520 6e65 7874 2063 6f70 in the next cop\n-0000fb80: 792c 2074 6865 2028 6b2b 3129 7374 2c20 y, the (k+1)st, \n-0000fb90: 6172 6520 505f 3127 2c20 505f 3227 2c20 are P_1', P_2', \n-0000fba0: 2e2e 2e2c 2050 5f6d 272c 2074 6865 6e0a ..., P_m', then.\n-0000fbb0: 7468 6520 7665 7274 6578 206f 7264 6572 the vertex order\n-0000fbc0: 206f 6620 7468 6520 6765 6e65 7261 7465 of the generate\n-0000fbd0: 6420 706f 6c79 676f 6e73 2069 730a 2020 d polygons is. \n-0000fbe0: 2020 2042 6f64 7920 706f 6c79 676f 6e20 Body polygon \n-0000fbf0: 313a 2050 5f32 2050 5f31 2050 5f31 2720 1: P_2 P_1 P_1' \n-0000fc00: 505f 3227 0a20 2020 2020 426f 6479 2070 P_2'. Body p\n-0000fc10: 6f6c 7967 6f6e 2032 3a20 505f 3320 505f olygon 2: P_3 P_\n-0000fc20: 3220 505f 3227 2050 5f33 270a 2020 2020 2 P_2' P_3'. \n-0000fc30: 202e 2e2e 0a20 2020 2020 426f 6479 2070 .... Body p\n-0000fc40: 6f6c 7967 6f6e 206d 2d31 3a20 505f 6d20 olygon m-1: P_m \n-0000fc50: 505f 7b6d 2d31 7d20 505f 7b6d 2d31 7d27 P_{m-1} P_{m-1}'\n-0000fc60: 2050 5f6d 270a 0a20 2020 4f70 7469 6f6e P_m'.. Option\n-0000fc70: 7320 6f66 2075 6e63 6c6f 7365 6420 6c69 s of unclosed li\n-0000fc80: 6e65 2073 7765 6570 7320 6172 6520 636f ne sweeps are co\n-0000fc90: 7069 6564 2074 6f20 6561 6368 206f 7574 pied to each out\n-0000fca0: 7075 7420 706f 6c79 676f 6e2e 0a4f 7074 put polygon..Opt\n-0000fcb0: 696f 6e73 206f 6620 7468 6520 7377 6570 ions of the swep\n-0000fcc0: 7420 6c69 6e65 2061 7265 2069 676e 6f72 t line are ignor\n-0000fcd0: 6564 2e0a 0a20 2020 5768 656e 2074 6865 ed... When the\n-0000fce0: 7265 205f 6973 5f20 6120 636c 6f73 7572 re _is_ a closur\n-0000fcf0: 6520 7461 672c 2074 6865 6e20 e280 9873 e tag, then ...s\n-0000fd00: 7765 6570 e280 9920 636f 6e6e 6563 7473 weep... connects\n-0000fd10: 204e 2073 7563 6365 7373 6976 650a 636f N successive.co\n-0000fd20: 7069 6573 206f 6620 7468 6520 706f 6c79 pies of the poly\n-0000fd30: 6c69 6e65 2028 696e 636c 7564 696e 6720 line (including \n-0000fd40: 7468 6520 6f72 6967 696e 616c 2920 7769 the original) wi\n-0000fd50: 7468 2066 6f75 722d 7369 6465 6420 626f th four-sided bo\n-0000fd60: 6479 0a70 6f6c 7967 6f6e 7320 6a75 7374 dy.polygons just\n-0000fd70: 2061 7320 7468 6520 6361 7365 2077 6974 as the case wit\n-0000fd80: 6820 6e6f 2063 6c6f 7375 7265 2074 6167 h no closure tag\n-0000fd90: 2e20 2049 7420 7468 656e 2063 6f6e 6e65 . It then conne\n-0000fda0: 6374 7320 7468 650a 6c61 7374 2063 6f70 cts the.last cop\n-0000fdb0: 7920 6261 636b 2074 6f20 7468 6520 6f72 y back to the or\n-0000fdc0: 6967 696e 616c 2074 6f20 666f 726d 2061 iginal to form a\n-0000fdd0: 2072 6962 626f 6e2d 7368 6170 6564 2073 ribbon-shaped s\n-0000fde0: 7572 6661 6365 2074 6861 740a 636c 6f73 urface that.clos\n-0000fdf0: 6573 206f 6e20 6974 7365 6c66 2077 6974 es on itself wit\n-0000fe00: 6820 7477 6f20 686f 6c65 7320 7265 6d61 h two holes rema\n-0000fe10: 696e 696e 672e 0a0a 2020 2046 696e 616c ining... Final\n-0000fe20: 6c79 2c20 7468 6520 7377 6565 7020 6164 ly, the sweep ad\n-0000fe30: 6473 2074 776f 206d 6f72 6520 706f 6c79 ds two more poly\n-0000fe40: 676f 6e73 2074 6f20 7365 616c 2074 6865 gons to seal the\n-0000fe50: 2068 6f6c 6573 2061 6e64 2066 6f72 6d0a holes and form.\n-0000fe60: 6120 636c 6f73 6564 2073 7572 6661 6365 a closed surface\n-0000fe70: 2074 6861 742c 2064 6570 656e 6469 6e67 that, depending\n-0000fe80: 206f 6e20 7468 6520 7377 6565 7020 7472 on the sweep tr\n-0000fe90: 616e 7366 6f72 6d73 2c20 6d61 7920 7265 ansforms, may re\n-0000fea0: 7072 6573 656e 740a 7468 6520 626f 756e present.the boun\n-0000feb0: 6461 7279 206f 6620 6120 736f 6c69 642e dary of a solid.\n-0000fec0: 2020 496e 2074 6869 7320 6d61 6e6e 6572 In this manner\n-0000fed0: 2c20 e280 9873 7765 6570 e280 9920 666f , ...sweep... fo\n-0000fee0: 726d 7320 7468 6520 626f 756e 6461 7279 rms the boundary\n-0000fef0: 206f 660a 6120 7468 7265 652d 6469 6d65 of.a three-dime\n-0000ff00: 6e73 696f 6e61 6c20 6f62 6a65 6374 2066 nsional object f\n-0000ff10: 726f 6d20 6120 6f6e 652d 6469 6d65 6e73 rom a one-dimens\n-0000ff20: 696f 6e61 6c20 706f 6c79 6c69 6e65 2e20 ional polyline. \n-0000ff30: 2057 6520 6361 6c6c 0a74 6865 7365 2068 We call.these h\n-0000ff40: 6f6c 652d 6669 6c6c 696e 6720 706f 6c79 ole-filling poly\n-0000ff50: 676f 6e73 20e2 809c 656e 6473 e280 9d2e gons ...ends....\n-0000ff60: 0a0a 2020 2054 6865 206f 7264 6572 206f .. The order o\n-0000ff70: 6620 7665 7274 6963 6573 206f 6620 656e f vertices of en\n-0000ff80: 6420 706f 6c79 676f 6e73 2069 7320 696d d polygons is im\n-0000ff90: 706f 7274 616e 7420 666f 7220 636f 7272 portant for corr\n-0000ffa0: 6563 740a 6375 6c6c 696e 6720 6173 2064 ect.culling as d\n-0000ffb0: 6573 6372 6962 6564 2061 626f 7665 2e20 escribed above. \n-0000ffc0: 2049 6620 505f 315e 312c 2050 5f31 5e32 If P_1^1, P_1^2\n-0000ffd0: 2c20 2e2e 2e2c 2050 5f31 5e6e 2061 7265 , ..., P_1^n are\n-0000ffe0: 2074 6865 204e 0a63 6f70 6965 7320 6f66 the N.copies of\n-0000fff0: 2074 6865 2066 6972 7374 2070 6f6c 796c the first polyl\n-00010000: 696e 6520 706f 696e 7420 616e 6420 505f ine point and P_\n-00010010: 6d5e 312c 2050 5f6d 5e32 2c20 2e2e 2e20 m^1, P_m^2, ... \n-00010020: 2c50 5f6d 5e6e 2061 7265 2074 6865 0a4e ,P_m^n are the.N\n-00010030: 2063 6f70 6965 7320 6f66 2074 6865 206c copies of the l\n-00010040: 6173 7420 706f 6c79 6c69 6e65 2070 6f69 ast polyline poi\n-00010050: 6e74 2c20 7468 656e 2074 6865 2065 6e64 nt, then the end\n-00010060: 2070 6f6c 7967 6f6e 2076 6572 7465 7820 polygon vertex \n-00010070: 6f72 6465 720a 6973 0a20 2020 2020 456e order.is. En\n-00010080: 6420 706f 6c79 676f 6e20 313a 2050 5f31 d polygon 1: P_1\n-00010090: 5e6e 2c20 505f 315e 7b6e 2d31 7d2c 202e ^n, P_1^{n-1}, .\n-000100a0: 2e2e 202c 505f 315e 310a 2020 2020 2045 .. ,P_1^1. E\n-000100b0: 6e64 2070 6f6c 7967 6f6e 2032 3a20 505f nd polygon 2: P_\n-000100c0: 6d5e 312c 2050 5f6d 5e32 2c20 2e2e 2e20 m^1, P_m^2, ... \n-000100d0: 2c50 5f6d 5e6e 0a0a 2020 2049 6620 7468 ,P_m^n.. If th\n-000100e0: 6572 6520 6172 6520 6e6f 206f 7074 696f ere are no optio\n-000100f0: 6e73 206f 6e20 7468 6520 7377 6570 7420 ns on the swept \n-00010100: 6c69 6e65 2c20 7468 656e 2074 6865 20e2 line, then the .\n-00010110: 8098 7377 6565 70e2 8099 206f 7074 696f ..sweep... optio\n-00010120: 6e73 0a61 7265 2063 6f70 6965 6420 746f ns.are copied to\n-00010130: 2065 6163 6820 6f75 7470 7574 2070 6f6c each output pol\n-00010140: 7967 6f6e 2e20 2049 6620 7468 6520 7377 ygon. If the sw\n-00010150: 6570 7420 6c69 6e65 2064 6f65 7320 6861 ept line does ha\n-00010160: 7665 206f 7074 696f 6e73 2c0a 7468 6573 ve options,.thes\n-00010170: 6520 6172 6520 636f 7069 6564 2074 6f20 e are copied to \n-00010180: 636f 7272 6573 706f 6e64 696e 6720 626f corresponding bo\n-00010190: 6479 2070 6f6c 7967 6f6e 733b 2074 6865 dy polygons; the\n-000101a0: 2073 7765 6570 206f 7074 696f 6e73 2061 sweep options a\n-000101b0: 7265 0a63 6f70 6965 6420 746f 2074 6865 re.copied to the\n-000101c0: 2065 6e64 2070 6f6c 7967 6f6e 732e 2020 end polygons. \n-000101d0: 496e 2074 6869 7320 6d61 6e6e 6572 2c20 In this manner, \n-000101e0: 626f 6479 2061 6e64 2065 6e64 7320 6d61 body and ends ma\n-000101f0: 7920 6265 2064 7261 776e 0a77 6974 6820 y be drawn.with \n-00010200: 6469 6666 6572 656e 7420 6368 6172 6163 different charac\n-00010210: 7465 7269 7374 6963 7320 7375 6368 2061 teristics such a\n-00010220: 7320 e280 9866 696c 6c63 6f6c 6f72 e280 s ...fillcolor..\n-00010230: 992e 0a0a 1f0a 4669 6c65 3a20 736b 6574 ......File: sket\n-00010240: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n-00010250: 5377 6570 7420 706f 6c79 676f 6e73 2c20 Swept polygons, \n-00010260: 204e 6578 743a 2053 7765 7074 2062 6c6f Next: Swept blo\n-00010270: 636b 732c 2020 5072 6576 3a20 5377 6570 cks, Prev: Swep\n-00010280: 7420 6c69 6e65 732c 2020 5570 3a20 5377 t lines, Up: Sw\n-00010290: 6565 7073 0a0a 332e 322e 362e 3320 5377 eeps..3.2.6.3 Sw\n-000102a0: 6570 7420 706f 6c79 676f 6e73 0a2e 2e2e ept polygons....\n+0000e070: 2020 2044 7261 7720 6f6e 6520 6f62 6a65 Draw one obje\n+0000e080: 6374 2074 7261 6e73 666f 726d 6564 2e0a ct transformed..\n+0000e090: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n+0000e0a0: 696e 666f 2c20 204e 6f64 653a 2044 6f74 info, Node: Dot\n+0000e0b0: 732c 2020 4e65 7874 3a20 4c69 6e65 732c s, Next: Lines,\n+0000e0c0: 2020 5072 6576 3a20 4472 6177 6162 6c65 Prev: Drawable\n+0000e0d0: 732c 2020 5570 3a20 4472 6177 6162 6c65 s, Up: Drawable\n+0000e0e0: 730a 0a33 2e32 2e31 2044 6f74 730a 2d2d s..3.2.1 Dots.--\n+0000e0f0: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 --------..*Synta\n+0000e100: 783a 2a0a 2020 2020 2064 6f74 735b 4f50 x:*. dots[OP\n+0000e110: 5449 4f4e 535d 2050 4f49 4e54 5f4c 4953 TIONS] POINT_LIS\n+0000e120: 540a 5468 6973 2063 6f6d 6d61 6e64 2069 T.This command i\n+0000e130: 7320 7468 6520 7468 7265 652d 6469 6d65 s the three-dime\n+0000e140: 6e73 696f 6e61 6c20 6571 7569 7661 6c65 nsional equivale\n+0000e150: 6e74 206f 6620 7468 6520 e280 9850 5354 nt of the ...PST\n+0000e160: 7269 636b 73e2 8099 0a63 6f6d 6d61 6e64 ricks....command\n+0000e170: 20e2 8098 5c70 7364 6f74 73e2 8099 2e0a ...\\psdots.....\n+0000e180: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n+0000e190: 696e 666f 2c20 204e 6f64 653a 204c 696e info, Node: Lin\n+0000e1a0: 6573 2c20 204e 6578 743a 2043 7572 7665 es, Next: Curve\n+0000e1b0: 732c 2020 5072 6576 3a20 446f 7473 2c20 s, Prev: Dots, \n+0000e1c0: 2055 703a 2044 7261 7761 626c 6573 0a0a Up: Drawables..\n+0000e1d0: 332e 322e 3220 4c69 6e65 730a 2d2d 2d2d 3.2.2 Lines.----\n+0000e1e0: 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 6178 -------..*Syntax\n+0000e1f0: 3a2a 0a20 2020 2020 6c69 6e65 5b4f 5054 :*. line[OPT\n+0000e200: 494f 4e53 5d20 504f 494e 545f 4c49 5354 IONS] POINT_LIST\n+0000e210: 0a54 6869 7320 636f 6d6d 616e 6420 6973 .This command is\n+0000e220: 2074 6865 2074 6872 6565 2d64 696d 656e the three-dimen\n+0000e230: 7369 6f6e 616c 2065 7175 6976 616c 656e sional equivalen\n+0000e240: 7420 6f66 2074 6865 20e2 8098 5053 5472 t of the ...PSTr\n+0000e250: 6963 6b73 e280 990a 636f 6d6d 616e 6420 icks....command \n+0000e260: e280 985c 7073 6c69 6e65 e280 992e 0a0a ...\\psline......\n+0000e270: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+0000e280: 6e66 6f2c 2020 4e6f 6465 3a20 4375 7276 nfo, Node: Curv\n+0000e290: 6573 2c20 204e 6578 743a 2050 6f6c 7967 es, Next: Polyg\n+0000e2a0: 6f6e 732c 2020 5072 6576 3a20 4c69 6e65 ons, Prev: Line\n+0000e2b0: 732c 2020 5570 3a20 4472 6177 6162 6c65 s, Up: Drawable\n+0000e2c0: 730a 0a33 2e32 2e33 2043 7572 7665 730a s..3.2.3 Curves.\n+0000e2d0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 ------------..*S\n+0000e2e0: 796e 7461 783a 2a0a 2020 2020 2063 7572 yntax:*. cur\n+0000e2f0: 7665 5b4f 5054 494f 4e53 5d20 504f 494e ve[OPTIONS] POIN\n+0000e300: 545f 4c49 5354 0a54 6869 7320 636f 6d6d T_LIST.This comm\n+0000e310: 616e 6420 6973 2074 6865 2074 6872 6565 and is the three\n+0000e320: 2d64 696d 656e 7369 6f6e 616c 2065 7175 -dimensional equ\n+0000e330: 6976 616c 656e 7420 6f66 2074 6865 20e2 ivalent of the .\n+0000e340: 8098 5053 5472 6963 6b73 e280 990a 636f ..PSTricks....co\n+0000e350: 6d6d 616e 6420 e280 985c 7073 6375 7276 mmand ...\\pscurv\n+0000e360: 65e2 8099 2e20 2049 7420 6973 206e 6f74 e.... It is not\n+0000e370: 2069 6d70 6c65 6d65 6e74 6564 2069 6e20 implemented in \n+0000e380: 7468 6520 6375 7272 656e 7420 7665 7273 the current vers\n+0000e390: 696f 6e20 6f66 0ae2 8098 736b 6574 6368 ion of....sketch\n+0000e3a0: e280 992e 0a0a 1f0a 4669 6c65 3a20 736b ........File: sk\n+0000e3b0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+0000e3c0: 3a20 506f 6c79 676f 6e73 2c20 204e 6578 : Polygons, Nex\n+0000e3d0: 743a 2053 7065 6369 616c 732c 2020 5072 t: Specials, Pr\n+0000e3e0: 6576 3a20 4375 7276 6573 2c20 2055 703a ev: Curves, Up:\n+0000e3f0: 2044 7261 7761 626c 6573 0a0a 332e 322e Drawables..3.2.\n+0000e400: 3420 506f 6c79 676f 6e73 0a2d 2d2d 2d2d 4 Polygons.-----\n+0000e410: 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 6e74 ---------..*Synt\n+0000e420: 6178 3a2a 0a20 2020 2020 706f 6c79 676f ax:*. polygo\n+0000e430: 6e5b 4f50 5449 4f4e 535d 2050 4f49 4e54 n[OPTIONS] POINT\n+0000e440: 5f4c 4953 540a 5468 6973 2063 6f6d 6d61 _LIST.This comma\n+0000e450: 6e64 2069 7320 7468 6520 7468 7265 652d nd is the three-\n+0000e460: 6469 6d65 6e73 696f 6e61 6c20 6571 7569 dimensional equi\n+0000e470: 7661 6c65 6e74 206f 6620 7468 6520 e280 valent of the ..\n+0000e480: 9850 5354 7269 636b 73e2 8099 0a63 6f6d .PSTricks....com\n+0000e490: 6d61 6e64 20e2 8098 5c70 7370 6f6c 7967 mand ...\\pspolyg\n+0000e4a0: 6f6e e280 992e 2020 5468 6520 e280 9873 on.... The ...s\n+0000e4b0: 6b65 7463 68e2 8099 2068 6964 6465 6e20 ketch... hidden \n+0000e4c0: 7375 7266 6163 6520 616c 676f 7269 7468 surface algorith\n+0000e4d0: 6d20 6173 7375 6d65 730a 7468 6174 2070 m assumes.that p\n+0000e4e0: 6f6c 7967 6f6e 7320 6172 6520 636f 6e76 olygons are conv\n+0000e4f0: 6578 2061 6e64 2070 6c61 6e61 722e 2020 ex and planar. \n+0000e500: 496e 2070 7261 6374 6963 652c 2064 7261 In practice, dra\n+0000e510: 7769 6e67 7320 6d61 7920 7765 6c6c 0a74 wings may well.t\n+0000e520: 7572 6e20 6f75 7420 636f 7272 6563 746c urn out correctl\n+0000e530: 7920 6576 656e 2069 6620 7468 6573 6520 y even if these \n+0000e540: 6173 7375 6d70 7469 6f6e 7320 6172 6520 assumptions are \n+0000e550: 7669 6f6c 6174 6564 2e0a 0a1f 0a46 696c violated.....Fil\n+0000e560: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+0000e570: 204e 6f64 653a 2053 7065 6369 616c 732c Node: Specials,\n+0000e580: 2020 4e65 7874 3a20 5377 6565 7073 2c20 Next: Sweeps, \n+0000e590: 2050 7265 763a 2050 6f6c 7967 6f6e 732c Prev: Polygons,\n+0000e5a0: 2020 5570 3a20 4472 6177 6162 6c65 730a Up: Drawables.\n+0000e5b0: 0a33 2e32 2e35 2053 7065 6369 616c 730a .3.2.5 Specials.\n+0000e5c0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a --------------..\n+0000e5d0: 2a53 796e 7461 783a 2a0a 2020 2020 2073 *Syntax:*. s\n+0000e5e0: 7065 6369 616c 2024 5241 575f 5445 5854 pecial $RAW_TEXT\n+0000e5f0: 245b 4f50 5449 4f4e 535d 2041 5247 5f4c $[OPTIONS] ARG_L\n+0000e600: 4953 540a 4865 7265 20e2 8098 24e2 8099 IST.Here ...$...\n+0000e610: 2063 616e 2062 6520 616e 7920 6368 6172 can be any char\n+0000e620: 6163 7465 7220 616e 6420 6973 2075 7365 acter and is use\n+0000e630: 6420 746f 2064 656c 696d 6974 2074 6865 d to delimit the\n+0000e640: 2073 7461 7274 2061 6e64 2065 6e64 0a6f start and end.o\n+0000e650: 6620 5241 575f 5445 5854 2e20 2054 6865 f RAW_TEXT. The\n+0000e660: 2063 6f6d 6d61 6e64 2065 6d62 6564 7320 command embeds \n+0000e670: 5241 575f 5445 5854 2069 6e20 7468 6520 RAW_TEXT in the \n+0000e680: e280 9873 6b65 7463 68e2 8099 206f 7574 ...sketch... out\n+0000e690: 7075 7420 6166 7465 720a 7065 7266 6f72 put after.perfor\n+0000e6a0: 6d69 6e67 2073 7562 7374 6974 7574 696f ming substitutio\n+0000e6b0: 6e73 2061 7320 666f 6c6c 6f77 732e 0a20 ns as follows.. \n+0000e6c0: 2020 e280 a220 e280 9823 49e2 8099 2077 ... ...#I... w\n+0000e6d0: 6865 7265 2049 2069 7320 6120 706f 7369 here I is a posi\n+0000e6e0: 7469 7665 2069 6e74 6567 6572 2069 7320 tive integer is \n+0000e6f0: 7265 706c 6163 6564 2062 7920 7468 6520 replaced by the \n+0000e700: 4927 7468 2076 616c 7565 2069 6e0a 2020 I'th value in. \n+0000e710: 2020 2041 5247 5f4c 4953 542e 2020 506f ARG_LIST. Po\n+0000e720: 696e 7420 616e 6420 7665 6374 6f72 2061 int and vector a\n+0000e730: 7267 756d 656e 7473 2062 6563 6f6d 6520 rguments become \n+0000e740: 7477 6f2d 6469 6d65 6e73 696f 6e61 6c0a two-dimensional.\n+0000e750: 2020 2020 2070 6f69 6e74 732c 2077 6869 points, whi\n+0000e760: 6368 2061 7265 2074 6865 2074 7261 6e73 ch are the trans\n+0000e770: 666f 726d 6564 2033 6420 6172 6775 6d65 formed 3d argume\n+0000e780: 6e74 7320 7072 6f6a 6563 7465 6420 6f6e nts projected on\n+0000e790: 746f 2074 6865 0a20 2020 2020 582d 5920 to the. X-Y \n+0000e7a0: 706c 616e 652e 2020 5468 6973 2061 6c6c plane. This all\n+0000e7b0: 6f77 7320 7477 6f2d 6469 6d65 6e74 696f ows two-dimentio\n+0000e7c0: 6e61 6c20 6f75 7470 7574 2065 6c65 6d65 nal output eleme\n+0000e7d0: 6e74 7320 7375 6368 2061 730a 2020 2020 nts such as. \n+0000e7e0: 206c 6162 656c 7320 746f 2062 6520 6561 labels to be ea\n+0000e7f0: 7369 6c79 2070 6f73 6974 696f 6e65 6420 sily positioned \n+0000e800: 7769 7468 2072 6573 7065 6374 2074 6f20 with respect to \n+0000e810: 7468 7265 652d 6469 6d65 6e73 696f 6e61 three-dimensiona\n+0000e820: 6c0a 2020 2020 2066 6561 7475 7265 7320 l. features \n+0000e830: 696e 2074 6865 2064 7261 7769 6e67 2e20 in the drawing. \n+0000e840: 2053 6361 6c61 7220 6172 6775 6d65 6e74 Scalar argument\n+0000e850: 7320 6172 6520 7375 6273 6974 7574 6564 s are subsituted\n+0000e860: 2064 6972 6563 746c 792e 0a20 2020 2020 directly.. \n+0000e870: 4e6f 2074 7261 6e73 666f 726d 6174 696f No transformatio\n+0000e880: 6e20 6973 2061 7070 6c69 6564 2e0a 2020 n is applied.. \n+0000e890: 20e2 80a2 20e2 8098 237b 497d e280 9920 ... ...#{I}... \n+0000e8a0: 6973 2061 6c73 6f20 7265 706c 6163 6564 is also replaced\n+0000e8b0: 2061 7320 6162 6f76 652e 0a20 2020 e280 as above.. ..\n+0000e8c0: a220 e280 9823 4927 32e2 8099 2069 7320 . ...#I'2... is \n+0000e8d0: 7265 706c 6163 6564 2061 7320 6162 6f76 replaced as abov\n+0000e8e0: 6520 666f 7220 706f 696e 7473 206f 7220 e for points or \n+0000e8f0: 7665 6374 6f72 732e 2020 4974 2069 7320 vectors. It is \n+0000e900: 616e 2065 7272 6f72 0a20 2020 2020 666f an error. fo\n+0000e910: 7220 7468 6520 4927 7468 2061 7267 756d r the I'th argum\n+0000e920: 656e 7420 746f 2062 6520 6120 7363 616c ent to be a scal\n+0000e930: 6172 2e0a 2020 20e2 80a2 20e2 8098 2349 ar.. ... ...#I\n+0000e940: 2778 e280 992c 20e2 8098 2349 2779 e280 'x..., ...#I'y..\n+0000e950: 992c 206f 7220 e280 9823 4927 7ae2 8099 ., or ...#I'z...\n+0000e960: 2069 7320 7265 706c 6163 6564 2c20 7265 is replaced, re\n+0000e970: 7370 6563 7469 7665 6c79 2c20 6279 2074 spectively, by t\n+0000e980: 6865 2073 6361 6c61 720a 2020 2020 2058 he scalar. X\n+0000e990: 2c20 592c 206f 7220 5a2d 636f 6f72 6469 , Y, or Z-coordi\n+0000e9a0: 6e61 7465 206f 6620 7468 6520 6172 6775 nate of the argu\n+0000e9b0: 6d65 6e74 2070 6f69 6e74 206f 7220 7665 ment point or ve\n+0000e9c0: 6374 6f72 2e20 2049 7420 6973 2061 6e0a ctor. It is an.\n+0000e9d0: 2020 2020 2065 7272 6f72 2066 6f72 2074 error for t\n+0000e9e0: 6865 2049 2774 6820 6172 6775 6d65 6e74 he I'th argument\n+0000e9f0: 2074 6f20 6265 2061 2073 6361 6c61 722e to be a scalar.\n+0000ea00: 0a20 2020 e280 a220 e280 9823 4927 33e2 . ... ...#I'3.\n+0000ea10: 8099 2069 7320 7265 706c 6163 6564 2062 .. is replaced b\n+0000ea20: 7920 7468 6520 7468 7265 652d 6469 6d65 y the three-dime\n+0000ea30: 6e73 696f 6e61 6c20 7472 616e 7366 6f72 nsional transfor\n+0000ea40: 6d65 6420 6172 6775 6d65 6e74 2e0a 2020 med argument.. \n+0000ea50: 2020 204e 6f74 6520 7468 6174 2069 6620 Note that if \n+0000ea60: 6120 7065 7273 7065 6374 6976 6520 7472 a perspective tr\n+0000ea70: 616e 7366 6f72 6d61 7469 6f6e 2068 6173 ansformation has\n+0000ea80: 2062 6565 6e20 6170 706c 6965 642c 2074 been applied, t\n+0000ea90: 6865 0a20 2020 2020 5a2d 636f 6f72 6469 he. Z-coordi\n+0000eaa0: 6e61 7465 2068 6173 206c 6974 746c 6520 nate has little \n+0000eab0: 6765 6f6d 6574 7269 6320 7369 676e 6966 geometric signif\n+0000eac0: 6963 616e 6365 2c20 7468 6f75 6768 2069 icance, though i\n+0000ead0: 740a 2020 2020 2061 6363 7572 6174 656c t. accuratel\n+0000eae0: 7920 696e 6469 6361 7465 7320 7265 6c61 y indicates rela\n+0000eaf0: 7469 7665 2064 6570 7468 2e0a 2020 20e2 tive depth.. .\n+0000eb00: 80a2 20e2 8098 2349 2d4a e280 9920 7768 .. ...#I-J... wh\n+0000eb10: 6572 6520 4920 616e 6420 4a20 6172 6520 ere I and J are \n+0000eb20: 706f 7369 7469 7665 2069 6e74 6567 6572 positive integer\n+0000eb30: 7320 6973 2072 6570 6c61 6365 6420 6279 s is replaced by\n+0000eb40: 2061 2073 7472 696e 670a 2020 2020 20e2 a string. .\n+0000eb50: 8098 7b41 4e47 4c45 7de2 8099 2077 6865 ..{ANGLE}... whe\n+0000eb60: 7265 2041 4e47 4c45 2069 7320 7468 6520 re ANGLE is the \n+0000eb70: 706f 6c61 7220 616e 676c 6520 6f66 2061 polar angle of a\n+0000eb80: 2076 6563 746f 7220 6672 6f6d 2074 6865 vector from the\n+0000eb90: 2049 2774 680a 2020 2020 2070 6f69 6e74 I'th. point\n+0000eba0: 2069 6e20 504f 494e 545f 4c49 5354 2074 in POINT_LIST t\n+0000ebb0: 6f20 7468 6520 4a27 7468 2070 6f69 6e74 o the J'th point\n+0000ebc0: 2070 726f 6a65 6374 6564 2069 6e74 6f20 projected into \n+0000ebd0: 7468 6520 782d 7920 706c 616e 652e 0a20 the x-y plane.. \n+0000ebe0: 2020 2020 4974 2069 7320 616e 2065 7272 It is an err\n+0000ebf0: 6f72 2066 6f72 2074 6865 2049 2774 6820 or for the I'th \n+0000ec00: 6f72 204a 2774 6820 6172 6775 6d65 6e74 or J'th argument\n+0000ec10: 2074 6f20 6265 2061 2073 6361 6c61 7220 to be a scalar \n+0000ec20: 6f72 2061 0a20 2020 2020 7665 6374 6f72 or a. vector\n+0000ec30: 2e0a 2020 20e2 80a2 20e2 8098 237b 492d .. ... ...#{I-\n+0000ec40: 4a7d e280 9920 6973 2061 6c73 6f20 7265 J}... is also re\n+0000ec50: 706c 6163 6564 2061 7320 6162 6f76 652e placed as above.\n+0000ec60: 0a20 2020 e280 a220 e280 9823 23e2 8099 . ... ...##...\n+0000ec70: 2069 7320 7265 706c 6163 6564 2077 6974 is replaced wit\n+0000ec80: 6820 e280 9823 e280 992e 0a54 6865 2066 h ...#.....The f\n+0000ec90: 6f72 6d73 2077 6974 6820 6272 6163 6573 orms with braces\n+0000eca0: 20e2 8098 7b20 7de2 8099 2061 7265 2075 ...{ }... are u\n+0000ecb0: 7365 6675 6c20 7768 656e 2074 6865 2061 seful when the a\n+0000ecc0: 7267 756d 656e 7420 6973 2069 6d6d 6564 rgument is immed\n+0000ecd0: 6961 7465 6c79 0a66 6f6c 6c6f 7765 6420 iately.followed \n+0000ece0: 6279 2061 2064 6967 6974 206f 7220 6120 by a digit or a \n+0000ecf0: 7469 636b 2063 6861 7261 6374 6572 2074 tick character t\n+0000ed00: 6861 7420 6973 2070 6172 7420 6f66 2074 hat is part of t\n+0000ed10: 6865 2054 6558 2063 6f64 652e 0a0a 2020 he TeX code... \n+0000ed20: 2054 6865 206f 6e6c 7920 7573 6566 756c The only useful\n+0000ed30: 206f 7074 696f 6e20 6f66 20e2 8098 7370 option of ...sp\n+0000ed40: 6563 6961 6ce2 8099 2069 7320 e280 986c ecial... is ...l\n+0000ed50: 6179 e280 992c 2077 6869 6368 2064 6574 ay..., which det\n+0000ed60: 6572 6d69 6e65 7320 6966 2074 6865 0a73 ermines if the.s\n+0000ed70: 7562 7374 6974 7565 6420 7261 7720 7465 ubstitued raw te\n+0000ed80: 7874 2069 7320 656d 6974 7465 6420 6265 xt is emitted be\n+0000ed90: 666f 7265 2c20 6166 7465 722c 206f 7220 fore, after, or \n+0000eda0: 7573 696e 6720 7468 6520 6669 7273 7420 using the first \n+0000edb0: 706f 696e 740a 696e 2050 4f49 4e54 5f4c point.in POINT_L\n+0000edc0: 4953 5420 6173 2061 6e20 696e 6469 6361 IST as an indica\n+0000edd0: 746f 7220 6f66 2064 6570 7468 2e20 2054 tor of depth. T\n+0000ede0: 6865 7365 206f 6363 7572 2c20 7265 7370 hese occur, resp\n+0000edf0: 6563 7469 7665 6c79 2c20 7769 7468 0ae2 ectively, with..\n+0000ee00: 8098 6c61 793d 756e 6465 72e2 8099 2c20 ..lay=under..., \n+0000ee10: e280 986c 6179 3d6f 7665 72e2 8099 2c20 ...lay=over..., \n+0000ee20: 616e 6420 e280 986c 6179 3d69 6ee2 8099 and ...lay=in...\n+0000ee30: 2e20 2053 6565 202a 6e6f 7465 2053 7065 . See *note Spe\n+0000ee40: 6369 616c 206f 626a 6563 7473 3a3a 2061 cial objects:: a\n+0000ee50: 6e64 0a2a 6e6f 7465 2054 696b 5a2f 5047 nd.*note TikZ/PG\n+0000ee60: 4620 7573 6572 2d64 6566 696e 6564 2073 F user-defined s\n+0000ee70: 7479 6c65 733a 3a20 666f 7220 6578 616d tyles:: for exam\n+0000ee80: 706c 6573 2e20 202a 4e6f 7465 2049 6e74 ples. *Note Int\n+0000ee90: 6572 6e61 6c0a 6f70 7469 6f6e 733a 3a2e ernal.options::.\n+0000eea0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n+0000eeb0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377 .info, Node: Sw\n+0000eec0: 6565 7073 2c20 204e 6578 743a 2042 6c6f eeps, Next: Blo\n+0000eed0: 636b 732c 2020 5072 6576 3a20 5370 6563 cks, Prev: Spec\n+0000eee0: 6961 6c73 2c20 2055 703a 2044 7261 7761 ials, Up: Drawa\n+0000eef0: 626c 6573 0a0a 332e 322e 3620 5377 6565 bles..3.2.6 Swee\n+0000ef00: 7073 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ps.------------.\n+0000ef10: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020 .*Syntax:*. \n+0000ef20: 7377 6565 7020 7b20 4e2c 2054 5f31 2c20 sweep { N, T_1, \n+0000ef30: 545f 322c 202e 2e2e 2c20 545f 5220 7d5b T_2, ..., T_R }[\n+0000ef40: 4f50 5449 4f4e 535d 2053 5745 5054 5f4f OPTIONS] SWEPT_O\n+0000ef50: 424a 4543 540a 2020 2020 2073 7765 6570 BJECT. sweep\n+0000ef60: 207b 204e 3c3e 2c20 545f 312c 2054 5f32 { N<>, T_1, T_2\n+0000ef70: 2c20 2e2e 2e2c 2054 5f52 207d 5b4f 5054 , ..., T_R }[OPT\n+0000ef80: 494f 4e53 5d20 5357 4550 545f 4f42 4a45 IONS] SWEPT_OBJE\n+0000ef90: 4354 0a54 6865 2073 7765 6570 2063 6f6e CT.The sweep con\n+0000efa0: 6e65 6374 7320 4e20 286f 7220 7065 7268 nects N (or perh\n+0000efb0: 6170 7320 4e2b 3129 2063 6f70 6965 7320 aps N+1) copies \n+0000efc0: 6f66 2053 5745 5054 5f4f 424a 4543 5420 of SWEPT_OBJECT \n+0000efd0: 696e 206f 7264 6572 2074 6f0a 6372 6561 in order to.crea\n+0000efe0: 7465 2061 206e 6577 206f 626a 6563 7420 te a new object \n+0000eff0: 6f66 2068 6967 6865 7220 6469 6d65 6e73 of higher dimens\n+0000f000: 696f 6e2e 2020 5468 6520 545f 4920 2866 ion. The T_I (f\n+0000f010: 6f72 2069 2062 6574 7765 656e 2031 2061 or i between 1 a\n+0000f020: 6e64 0a72 2920 6172 6520 7472 616e 7366 nd.r) are transf\n+0000f030: 6f72 6d73 2e20 2054 6865 206b 2774 6820 orms. The k'th \n+0000f040: 636f 7079 206f 6620 5357 4550 545f 4f42 copy of SWEPT_OB\n+0000f050: 4a45 4354 2069 7320 7072 6f64 7563 6564 JECT is produced\n+0000f060: 2062 790a 6170 706c 7969 6e67 2074 6865 by.applying the\n+0000f070: 2066 6f6c 6c6f 7769 6e67 2074 7261 6e73 following trans\n+0000f080: 666f 726d 2074 6f20 7468 6520 6f72 6967 form to the orig\n+0000f090: 696e 616c 2e0a 2020 2020 2054 5f31 5e6b inal.. T_1^k\n+0000f0a0: 2074 6865 6e20 545f 325e 6b20 7468 656e then T_2^k then\n+0000f0b0: 202e 2e2e 2074 6865 6e20 545f 525e 6b0a ... then T_R^k.\n+0000f0c0: 4865 7265 2054 5e6b 206d 6561 6e73 2022 Here T^k means \"\n+0000f0d0: 7472 616e 7366 6f72 6d20 5420 6170 706c transform T appl\n+0000f0e0: 6965 6420 6b20 7469 6d65 732e 2220 2054 ied k times.\" T\n+0000f0f0: 6865 206f 7269 6769 6e61 6c20 6f62 6a65 he original obje\n+0000f100: 6374 2069 730a 7468 6520 7a65 726f 2774 ct is.the zero't\n+0000f110: 6820 636f 7079 2c20 7769 7468 206b 3d30 h copy, with k=0\n+0000f120: 2061 6e64 2065 6666 6563 7469 7665 6c79 and effectively\n+0000f130: 206e 6f20 7472 616e 7366 6f72 6d20 6170 no transform ap\n+0000f140: 706c 6965 6420 2854 5e30 3d49 2c0a 7468 plied (T^0=I,.th\n+0000f150: 6520 6964 656e 7469 7479 2074 7261 6e73 e identity trans\n+0000f160: 666f 726d 292e 0a0a 2020 2054 6865 206d form)... The m\n+0000f170: 6574 686f 6420 6f66 2063 6f6e 6e65 6374 ethod of connect\n+0000f180: 696e 6720 7468 6520 636f 7069 6573 2064 ing the copies d\n+0000f190: 6570 656e 6473 206f 6e20 7468 6520 7479 epends on the ty\n+0000f1a0: 7065 206f 660a 5357 4550 545f 4f42 4a45 pe of.SWEPT_OBJE\n+0000f1b0: 4354 2061 6e64 206f 6e20 7768 6574 6865 CT and on whethe\n+0000f1c0: 7220 7468 6520 636c 6f73 7572 6520 7461 r the closure ta\n+0000f1d0: 6720 e280 983c 3ee2 8099 2069 7320 7072 g ...<>... is pr\n+0000f1e0: 6573 656e 7420 6f72 206e 6f74 2e0a 0a20 esent or not... \n+0000f1f0: 2020 416e 2065 7861 6d70 6c65 206f 6620 An example of \n+0000f200: 6120 7377 6565 7020 7768 6572 6520 723d a sweep where r=\n+0000f210: 3220 6973 2074 6865 204d 6f62 6975 7320 2 is the Mobius \n+0000f220: 6669 6775 7265 2061 7420 2a6e 6f74 6520 figure at *note \n+0000f230: 4d6f 7265 2074 6f0a 6c65 6172 6e3a 3a2e More to.learn::.\n+0000f240: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2053 7765 ..* Menu:..* Swe\n+0000f250: 7074 2070 6f69 6e74 733a 3a20 2020 2020 pt points:: \n+0000f260: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+0000f270: 2070 6f69 6e74 7320 6d61 6b65 206c 696e points make lin\n+0000f280: 6573 206f 7220 706f 6c79 676f 6e73 2e0a es or polygons..\n+0000f290: 2a20 5377 6570 7420 6c69 6e65 733a 3a20 * Swept lines:: \n+0000f2a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0000f2b0: 5377 6570 7420 6c69 6e65 7320 6d61 6b65 Swept lines make\n+0000f2c0: 206f 7065 6e20 6f72 2063 6c6f 7365 6420 open or closed \n+0000f2d0: 7375 7266 6163 6573 2e0a 2a20 5377 6570 surfaces..* Swep\n+0000f2e0: 7420 706f 6c79 676f 6e73 3a3a 2020 2020 t polygons:: \n+0000f2f0: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n+0000f300: 706f 6c79 676f 6e73 206d 616b 6520 636c polygons make cl\n+0000f310: 6f73 6564 2073 7572 6661 6365 732e 0a2a osed surfaces..*\n+0000f320: 2053 7765 7074 2062 6c6f 636b 733a 3a20 Swept blocks:: \n+0000f330: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+0000f340: 7765 7074 2062 6c6f 636b 20e2 89a1 2062 wept block ... b\n+0000f350: 6c6f 636b 206f 6620 7377 6565 7073 2e0a lock of sweeps..\n+0000f360: 2a20 5377 6565 7020 6661 6365 2073 706c * Sweep face spl\n+0000f370: 6974 7469 6e67 3a3a 2020 2020 2020 2020 itting:: \n+0000f380: 4669 7869 6e67 2077 6172 7065 6420 6661 Fixing warped fa\n+0000f390: 6365 7320 7769 7468 2074 7269 616e 676c ces with triangl\n+0000f3a0: 6573 2e0a 0a1f 0a46 696c 653a 2073 6b65 es.....File: ske\n+0000f3b0: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n+0000f3c0: 2053 7765 7074 2070 6f69 6e74 732c 2020 Swept points, \n+0000f3d0: 4e65 7874 3a20 5377 6570 7420 6c69 6e65 Next: Swept line\n+0000f3e0: 732c 2020 5072 6576 3a20 5377 6565 7073 s, Prev: Sweeps\n+0000f3f0: 2c20 2055 703a 2053 7765 6570 730a 0a33 , Up: Sweeps..3\n+0000f400: 2e32 2e36 2e31 2053 7765 7074 2070 6f69 .2.6.1 Swept poi\n+0000f410: 6e74 730a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e nts.............\n+0000f420: 2e2e 2e2e 2e2e 2e2e 0a0a 4966 2053 5745 ..........If SWE\n+0000f430: 5054 5f4f 424a 4543 5420 6973 2061 2070 PT_OBJECT is a p\n+0000f440: 6f69 6e74 206c 6973 7420 616e 6420 7468 oint list and th\n+0000f450: 6572 6520 6973 206e 6f20 636c 6f73 7572 ere is no closur\n+0000f460: 6520 7461 672c 2074 6865 6e0a e280 9873 e tag, then....s\n+0000f470: 7765 6570 e280 9920 636f 6e6e 6563 7473 weep... connects\n+0000f480: 204e 2b31 2073 7563 6365 7373 6976 6520 N+1 successive \n+0000f490: 636f 7069 6573 206f 6620 6561 6368 2070 copies of each p\n+0000f4a0: 6f69 6e74 2028 696e 636c 7564 696e 6720 oint (including \n+0000f4b0: 7468 650a 6f72 6967 696e 616c 2920 7769 the.original) wi\n+0000f4c0: 7468 2073 7472 6169 6768 7420 6c69 6e65 th straight line\n+0000f4d0: 2073 6567 6d65 6e74 7320 746f 2066 6f72 segments to for\n+0000f4e0: 6d20 6120 706f 6c79 6c69 6e65 2e20 2049 m a polyline. I\n+0000f4f0: 6620 7468 6572 6520 6172 650a 6d20 706f f there are.m po\n+0000f500: 696e 7473 2069 6e20 7468 6520 6f72 6967 ints in the orig\n+0000f510: 696e 616c 2070 6f69 6e74 206c 6973 742c inal point list,\n+0000f520: 2074 6865 6e20 6d20 706f 6c79 6c69 6e65 then m polyline\n+0000f530: 7320 7769 7468 204e 2073 6567 6d65 6e74 s with N segment\n+0000f540: 730a 6561 6368 2061 7265 2066 6f72 6d65 s.each are forme\n+0000f550: 6420 6279 2074 6865 2073 7765 6570 2e20 d by the sweep. \n+0000f560: 2049 6e20 7468 6973 206d 616e 6e65 722c In this manner,\n+0000f570: 20e2 8098 7377 6565 70e2 8099 2066 6f72 ...sweep... for\n+0000f580: 6d73 2061 2073 6574 206f 660a 6f6e 652d ms a set of.one-\n+0000f590: 6469 6d65 6e73 696f 6e61 6c20 6f62 6a65 dimensional obje\n+0000f5a0: 6374 7320 2870 6f6c 796c 696e 6573 2920 cts (polylines) \n+0000f5b0: 6672 6f6d 207a 6572 6f2d 6469 6d65 6e73 from zero-dimens\n+0000f5c0: 696f 6e61 6c20 6f6e 6573 2028 706f 696e ional ones (poin\n+0000f5d0: 7473 292e 0a0a 2020 2057 6865 6e20 7468 ts)... When th\n+0000f5e0: 6572 6520 5f69 735f 2061 2063 6c6f 7375 ere _is_ a closu\n+0000f5f0: 7265 2074 6167 2c20 e280 9873 7765 6570 re tag, ...sweep\n+0000f600: e280 9920 636f 6e6e 6563 7473 204e 2073 ... connects N s\n+0000f610: 7563 6365 7373 6976 6520 636f 7069 6573 uccessive copies\n+0000f620: 0a6f 6620 6561 6368 2070 6f69 6e74 2028 .of each point (\n+0000f630: 696e 636c 7564 696e 6720 7468 6520 6f72 including the or\n+0000f640: 6967 696e 616c 2920 7769 7468 2073 7472 iginal) with str\n+0000f650: 6169 6768 7420 6c69 6e65 2073 6567 6d65 aight line segme\n+0000f660: 6e74 7320 616e 640a 6669 6e61 6c6c 7920 nts and.finally \n+0000f670: 636f 6e6e 6563 7473 2074 6865 206c 6173 connects the las\n+0000f680: 7420 636f 7079 2062 6163 6b20 746f 2074 t copy back to t\n+0000f690: 6865 206f 7269 6769 6e61 6c20 746f 2066 he original to f\n+0000f6a0: 6f72 6d20 6120 706f 6c79 676f 6e0a 7769 orm a polygon.wi\n+0000f6b0: 7468 204e 2073 6964 6573 2e20 2049 6620 th N sides. If \n+0000f6c0: 7468 6572 6520 6172 6520 6d20 706f 696e there are m poin\n+0000f6d0: 7473 2069 6e20 7468 6520 6f72 6967 696e ts in the origin\n+0000f6e0: 616c 2070 6f69 6e74 206c 6973 742c 2074 al point list, t\n+0000f6f0: 6865 6e20 6d0a 706f 6c79 676f 6e73 2077 hen m.polygons w\n+0000f700: 6974 6820 4e20 7369 6465 7320 6561 6368 ith N sides each\n+0000f710: 2061 7265 2066 6f72 6d65 6420 6279 2074 are formed by t\n+0000f720: 6865 2073 7765 6570 2e20 2049 6e20 7468 he sweep. In th\n+0000f730: 6973 206d 616e 6e65 722c 0ae2 8098 7377 is manner,....sw\n+0000f740: 6565 70e2 8099 2066 6f72 6d73 2061 2073 eep... forms a s\n+0000f750: 6574 206f 6620 7477 6f2d 6469 6d65 6e73 et of two-dimens\n+0000f760: 696f 6e61 6c20 6f62 6a65 6374 7320 2870 ional objects (p\n+0000f770: 6f6c 7967 6f6e 7329 2066 726f 6d0a 7a65 olygons) from.ze\n+0000f780: 726f 2d64 696d 656e 7369 6f6e 616c 206f ro-dimensional o\n+0000f790: 6e65 7320 2870 6f69 6e74 7329 2e0a 0a20 nes (points)... \n+0000f7a0: 2020 4f70 7469 6f6e 7320 6f66 2074 6865 Options of the\n+0000f7b0: 20e2 8098 7377 6565 70e2 8099 2061 7265 ...sweep... are\n+0000f7c0: 2063 6f70 6965 6420 6469 7265 6374 6c79 copied directly\n+0000f7d0: 2074 6f20 7468 6520 7265 7375 6c74 696e to the resultin\n+0000f7e0: 670a 706f 6c79 6c69 6e65 2873 292e 0a0a g.polyline(s)...\n+0000f7f0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+0000f800: 6e66 6f2c 2020 4e6f 6465 3a20 5377 6570 nfo, Node: Swep\n+0000f810: 7420 6c69 6e65 732c 2020 4e65 7874 3a20 t lines, Next: \n+0000f820: 5377 6570 7420 706f 6c79 676f 6e73 2c20 Swept polygons, \n+0000f830: 2050 7265 763a 2053 7765 7074 2070 6f69 Prev: Swept poi\n+0000f840: 6e74 732c 2020 5570 3a20 5377 6565 7073 nts, Up: Sweeps\n+0000f850: 0a0a 332e 322e 362e 3220 5377 6570 7420 ..3.2.6.2 Swept \n+0000f860: 6c69 6e65 730a 2e2e 2e2e 2e2e 2e2e 2e2e lines...........\n+0000f870: 2e2e 2e2e 2e2e 2e2e 2e0a 0a49 6620 5357 ...........If SW\n+0000f880: 4550 545f 4f42 4a45 4354 2069 7320 6120 EPT_OBJECT is a \n+0000f890: 706f 6c79 6c69 6e65 2061 6e64 2074 6865 polyline and the\n+0000f8a0: 7265 2069 7320 6e6f 2063 6c6f 7375 7265 re is no closure\n+0000f8b0: 2074 6167 2c20 7468 656e 20e2 8098 7377 tag, then ...sw\n+0000f8c0: 6565 70e2 8099 0a63 6f6e 6e65 6374 7320 eep....connects \n+0000f8d0: 4e2b 3120 7375 6363 6573 7369 7665 2063 N+1 successive c\n+0000f8e0: 6f70 6965 7320 6f66 2074 6865 2070 6f6c opies of the pol\n+0000f8f0: 796c 696e 6520 2869 6e63 6c75 6469 6e67 yline (including\n+0000f900: 2074 6865 206f 7269 6769 6e61 6c29 0a77 the original).w\n+0000f910: 6974 6820 666f 7572 2d73 6964 6564 2070 ith four-sided p\n+0000f920: 6f6c 7967 6f6e 732c 2065 6163 6820 7061 olygons, each pa\n+0000f930: 6972 206f 6620 636f 7069 6573 2067 6976 ir of copies giv\n+0000f940: 696e 6720 7269 7365 2074 6f20 6120 2270 ing rise to a \"p\n+0000f950: 6f6c 7967 6f6e 0a73 7472 6970 2e22 2020 olygon.strip.\" \n+0000f960: 4966 2074 6865 7265 2061 7265 206d 2070 If there are m p\n+0000f970: 6f69 6e74 7320 696e 2074 6865 206f 7269 oints in the ori\n+0000f980: 6769 6e61 6c20 706f 6c79 6c69 6e65 2c20 ginal polyline, \n+0000f990: 7468 656e 2028 6d2d 3129 4e0a 706f 6c79 then (m-1)N.poly\n+0000f9a0: 676f 6e73 2061 7265 2066 6f72 6d65 6420 gons are formed \n+0000f9b0: 6279 2074 6865 2073 7765 6570 2e20 2057 by the sweep. W\n+0000f9c0: 6520 6361 6c6c 2074 6865 7365 20e2 809c e call these ...\n+0000f9d0: 626f 6479 2070 6f6c 7967 6f6e 73e2 809d body polygons...\n+0000f9e0: 2e20 2049 6e0a 7468 6973 206d 616e 6e65 . In.this manne\n+0000f9f0: 722c 20e2 8098 7377 6565 70e2 8099 2066 r, ...sweep... f\n+0000fa00: 6f72 6d73 2061 2074 776f 2d64 696d 656e orms a two-dimen\n+0000fa10: 7369 6f6e 616c 2073 7572 6661 6365 2066 sional surface f\n+0000fa20: 726f 6d20 6672 6f6d 2061 0a6f 6e65 2d64 rom from a.one-d\n+0000fa30: 696d 656e 7369 6f6e 616c 2070 6f6c 796c imensional polyl\n+0000fa40: 696e 652e 0a0a 2020 2054 6865 206f 7264 ine... The ord\n+0000fa50: 6572 206f 6620 7665 7274 6963 6573 2070 er of vertices p\n+0000fa60: 726f 6475 6365 6420 6279 20e2 8098 7377 roduced by ...sw\n+0000fa70: 6565 70e2 8099 2069 7320 696d 706f 7274 eep... is import\n+0000fa80: 616e 742e 2020 4966 2061 0a70 6f6c 7967 ant. If a.polyg\n+0000fa90: 6f6e 2773 2076 6572 7469 6365 7320 646f on's vertices do\n+0000faa0: 206e 6f74 2061 7070 6561 7220 696e 2063 not appear in c\n+0000fab0: 6f75 6e74 6572 2d63 6c6f 636b 7769 7365 ounter-clockwise\n+0000fac0: 206f 7264 6572 2069 6e20 7468 6520 6669 order in the fi\n+0000fad0: 6e61 6c0a 696d 6167 652c 2074 6865 2070 nal.image, the p\n+0000fae0: 6f6c 7967 6f6e 2077 696c 6c20 6265 2063 olygon will be c\n+0000faf0: 756c 6c65 6420 2875 6e6c 6573 7320 e280 ulled (unless ..\n+0000fb00: 9863 756c 6c3d 6661 6c73 65e2 8099 2069 .cull=false... i\n+0000fb10: 7320 7365 7429 2e20 2049 6620 7468 650a s set). If the.\n+0000fb20: 706f 696e 7473 2069 6e20 7468 6520 6b27 points in the k'\n+0000fb30: 7468 2063 6f70 7920 6f66 2074 6865 2070 th copy of the p\n+0000fb40: 6f6c 796c 696e 6520 6172 6520 505f 312c olyline are P_1,\n+0000fb50: 2050 5f32 2c20 2e2e 2e2c 2050 5f6d 2c20 P_2, ..., P_m, \n+0000fb60: 616e 6420 7468 650a 706f 696e 7473 2069 and the.points i\n+0000fb70: 6e20 7468 6520 6e65 7874 2063 6f70 792c n the next copy,\n+0000fb80: 2074 6865 2028 6b2b 3129 7374 2c20 6172 the (k+1)st, ar\n+0000fb90: 6520 505f 3127 2c20 505f 3227 2c20 2e2e e P_1', P_2', ..\n+0000fba0: 2e2c 2050 5f6d 272c 2074 6865 6e0a 7468 ., P_m', then.th\n+0000fbb0: 6520 7665 7274 6578 206f 7264 6572 206f e vertex order o\n+0000fbc0: 6620 7468 6520 6765 6e65 7261 7465 6420 f the generated \n+0000fbd0: 706f 6c79 676f 6e73 2069 730a 2020 2020 polygons is. \n+0000fbe0: 2042 6f64 7920 706f 6c79 676f 6e20 313a Body polygon 1:\n+0000fbf0: 2050 5f32 2050 5f31 2050 5f31 2720 505f P_2 P_1 P_1' P_\n+0000fc00: 3227 0a20 2020 2020 426f 6479 2070 6f6c 2'. Body pol\n+0000fc10: 7967 6f6e 2032 3a20 505f 3320 505f 3220 ygon 2: P_3 P_2 \n+0000fc20: 505f 3227 2050 5f33 270a 2020 2020 202e P_2' P_3'. .\n+0000fc30: 2e2e 0a20 2020 2020 426f 6479 2070 6f6c ... Body pol\n+0000fc40: 7967 6f6e 206d 2d31 3a20 505f 6d20 505f ygon m-1: P_m P_\n+0000fc50: 7b6d 2d31 7d20 505f 7b6d 2d31 7d27 2050 {m-1} P_{m-1}' P\n+0000fc60: 5f6d 270a 0a20 2020 4f70 7469 6f6e 7320 _m'.. Options \n+0000fc70: 6f66 2075 6e63 6c6f 7365 6420 6c69 6e65 of unclosed line\n+0000fc80: 2073 7765 6570 7320 6172 6520 636f 7069 sweeps are copi\n+0000fc90: 6564 2074 6f20 6561 6368 206f 7574 7075 ed to each outpu\n+0000fca0: 7420 706f 6c79 676f 6e2e 0a4f 7074 696f t polygon..Optio\n+0000fcb0: 6e73 206f 6620 7468 6520 7377 6570 7420 ns of the swept \n+0000fcc0: 6c69 6e65 2061 7265 2069 676e 6f72 6564 line are ignored\n+0000fcd0: 2e0a 0a20 2020 5768 656e 2074 6865 7265 ... When there\n+0000fce0: 205f 6973 5f20 6120 636c 6f73 7572 6520 _is_ a closure \n+0000fcf0: 7461 672c 2074 6865 6e20 e280 9873 7765 tag, then ...swe\n+0000fd00: 6570 e280 9920 636f 6e6e 6563 7473 204e ep... connects N\n+0000fd10: 2073 7563 6365 7373 6976 650a 636f 7069 successive.copi\n+0000fd20: 6573 206f 6620 7468 6520 706f 6c79 6c69 es of the polyli\n+0000fd30: 6e65 2028 696e 636c 7564 696e 6720 7468 ne (including th\n+0000fd40: 6520 6f72 6967 696e 616c 2920 7769 7468 e original) with\n+0000fd50: 2066 6f75 722d 7369 6465 6420 626f 6479 four-sided body\n+0000fd60: 0a70 6f6c 7967 6f6e 7320 6a75 7374 2061 .polygons just a\n+0000fd70: 7320 7468 6520 6361 7365 2077 6974 6820 s the case with \n+0000fd80: 6e6f 2063 6c6f 7375 7265 2074 6167 2e20 no closure tag. \n+0000fd90: 2049 7420 7468 656e 2063 6f6e 6e65 6374 It then connect\n+0000fda0: 7320 7468 650a 6c61 7374 2063 6f70 7920 s the.last copy \n+0000fdb0: 6261 636b 2074 6f20 7468 6520 6f72 6967 back to the orig\n+0000fdc0: 696e 616c 2074 6f20 666f 726d 2061 2072 inal to form a r\n+0000fdd0: 6962 626f 6e2d 7368 6170 6564 2073 7572 ibbon-shaped sur\n+0000fde0: 6661 6365 2074 6861 740a 636c 6f73 6573 face that.closes\n+0000fdf0: 206f 6e20 6974 7365 6c66 2077 6974 6820 on itself with \n+0000fe00: 7477 6f20 686f 6c65 7320 7265 6d61 696e two holes remain\n+0000fe10: 696e 672e 0a0a 2020 2046 696e 616c 6c79 ing... Finally\n+0000fe20: 2c20 7468 6520 7377 6565 7020 6164 6473 , the sweep adds\n+0000fe30: 2074 776f 206d 6f72 6520 706f 6c79 676f two more polygo\n+0000fe40: 6e73 2074 6f20 7365 616c 2074 6865 2068 ns to seal the h\n+0000fe50: 6f6c 6573 2061 6e64 2066 6f72 6d0a 6120 oles and form.a \n+0000fe60: 636c 6f73 6564 2073 7572 6661 6365 2074 closed surface t\n+0000fe70: 6861 742c 2064 6570 656e 6469 6e67 206f hat, depending o\n+0000fe80: 6e20 7468 6520 7377 6565 7020 7472 616e n the sweep tran\n+0000fe90: 7366 6f72 6d73 2c20 6d61 7920 7265 7072 sforms, may repr\n+0000fea0: 6573 656e 740a 7468 6520 626f 756e 6461 esent.the bounda\n+0000feb0: 7279 206f 6620 6120 736f 6c69 642e 2020 ry of a solid. \n+0000fec0: 496e 2074 6869 7320 6d61 6e6e 6572 2c20 In this manner, \n+0000fed0: e280 9873 7765 6570 e280 9920 666f 726d ...sweep... form\n+0000fee0: 7320 7468 6520 626f 756e 6461 7279 206f s the boundary o\n+0000fef0: 660a 6120 7468 7265 652d 6469 6d65 6e73 f.a three-dimens\n+0000ff00: 696f 6e61 6c20 6f62 6a65 6374 2066 726f ional object fro\n+0000ff10: 6d20 6120 6f6e 652d 6469 6d65 6e73 696f m a one-dimensio\n+0000ff20: 6e61 6c20 706f 6c79 6c69 6e65 2e20 2057 nal polyline. W\n+0000ff30: 6520 6361 6c6c 0a74 6865 7365 2068 6f6c e call.these hol\n+0000ff40: 652d 6669 6c6c 696e 6720 706f 6c79 676f e-filling polygo\n+0000ff50: 6e73 20e2 809c 656e 6473 e280 9d2e 0a0a ns ...ends......\n+0000ff60: 2020 2054 6865 206f 7264 6572 206f 6620 The order of \n+0000ff70: 7665 7274 6963 6573 206f 6620 656e 6420 vertices of end \n+0000ff80: 706f 6c79 676f 6e73 2069 7320 696d 706f polygons is impo\n+0000ff90: 7274 616e 7420 666f 7220 636f 7272 6563 rtant for correc\n+0000ffa0: 740a 6375 6c6c 696e 6720 6173 2064 6573 t.culling as des\n+0000ffb0: 6372 6962 6564 2061 626f 7665 2e20 2049 cribed above. I\n+0000ffc0: 6620 505f 315e 312c 2050 5f31 5e32 2c20 f P_1^1, P_1^2, \n+0000ffd0: 2e2e 2e2c 2050 5f31 5e6e 2061 7265 2074 ..., P_1^n are t\n+0000ffe0: 6865 204e 0a63 6f70 6965 7320 6f66 2074 he N.copies of t\n+0000fff0: 6865 2066 6972 7374 2070 6f6c 796c 696e he first polylin\n+00010000: 6520 706f 696e 7420 616e 6420 505f 6d5e e point and P_m^\n+00010010: 312c 2050 5f6d 5e32 2c20 2e2e 2e20 2c50 1, P_m^2, ... ,P\n+00010020: 5f6d 5e6e 2061 7265 2074 6865 0a4e 2063 _m^n are the.N c\n+00010030: 6f70 6965 7320 6f66 2074 6865 206c 6173 opies of the las\n+00010040: 7420 706f 6c79 6c69 6e65 2070 6f69 6e74 t polyline point\n+00010050: 2c20 7468 656e 2074 6865 2065 6e64 2070 , then the end p\n+00010060: 6f6c 7967 6f6e 2076 6572 7465 7820 6f72 olygon vertex or\n+00010070: 6465 720a 6973 0a20 2020 2020 456e 6420 der.is. End \n+00010080: 706f 6c79 676f 6e20 313a 2050 5f31 5e6e polygon 1: P_1^n\n+00010090: 2c20 505f 315e 7b6e 2d31 7d2c 202e 2e2e , P_1^{n-1}, ...\n+000100a0: 202c 505f 315e 310a 2020 2020 2045 6e64 ,P_1^1. End\n+000100b0: 2070 6f6c 7967 6f6e 2032 3a20 505f 6d5e polygon 2: P_m^\n+000100c0: 312c 2050 5f6d 5e32 2c20 2e2e 2e20 2c50 1, P_m^2, ... ,P\n+000100d0: 5f6d 5e6e 0a0a 2020 2049 6620 7468 6572 _m^n.. If ther\n+000100e0: 6520 6172 6520 6e6f 206f 7074 696f 6e73 e are no options\n+000100f0: 206f 6e20 7468 6520 7377 6570 7420 6c69 on the swept li\n+00010100: 6e65 2c20 7468 656e 2074 6865 20e2 8098 ne, then the ...\n+00010110: 7377 6565 70e2 8099 206f 7074 696f 6e73 sweep... options\n+00010120: 0a61 7265 2063 6f70 6965 6420 746f 2065 .are copied to e\n+00010130: 6163 6820 6f75 7470 7574 2070 6f6c 7967 ach output polyg\n+00010140: 6f6e 2e20 2049 6620 7468 6520 7377 6570 on. If the swep\n+00010150: 7420 6c69 6e65 2064 6f65 7320 6861 7665 t line does have\n+00010160: 206f 7074 696f 6e73 2c0a 7468 6573 6520 options,.these \n+00010170: 6172 6520 636f 7069 6564 2074 6f20 636f are copied to co\n+00010180: 7272 6573 706f 6e64 696e 6720 626f 6479 rresponding body\n+00010190: 2070 6f6c 7967 6f6e 733b 2074 6865 2073 polygons; the s\n+000101a0: 7765 6570 206f 7074 696f 6e73 2061 7265 weep options are\n+000101b0: 0a63 6f70 6965 6420 746f 2074 6865 2065 .copied to the e\n+000101c0: 6e64 2070 6f6c 7967 6f6e 732e 2020 496e nd polygons. In\n+000101d0: 2074 6869 7320 6d61 6e6e 6572 2c20 626f this manner, bo\n+000101e0: 6479 2061 6e64 2065 6e64 7320 6d61 7920 dy and ends may \n+000101f0: 6265 2064 7261 776e 0a77 6974 6820 6469 be drawn.with di\n+00010200: 6666 6572 656e 7420 6368 6172 6163 7465 fferent characte\n+00010210: 7269 7374 6963 7320 7375 6368 2061 7320 ristics such as \n+00010220: e280 9866 696c 6c63 6f6c 6f72 e280 992e ...fillcolor....\n+00010230: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n+00010240: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 5377 .info, Node: Sw\n+00010250: 6570 7420 706f 6c79 676f 6e73 2c20 204e ept polygons, N\n+00010260: 6578 743a 2053 7765 7074 2062 6c6f 636b ext: Swept block\n+00010270: 732c 2020 5072 6576 3a20 5377 6570 7420 s, Prev: Swept \n+00010280: 6c69 6e65 732c 2020 5570 3a20 5377 6565 lines, Up: Swee\n+00010290: 7073 0a0a 332e 322e 362e 3320 5377 6570 ps..3.2.6.3 Swep\n+000102a0: 7420 706f 6c79 676f 6e73 0a2e 2e2e 2e2e t polygons......\n 000102b0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-000102c0: 2e2e 2e0a 0a49 6620 5357 4550 545f 4f42 .....If SWEPT_OB\n-000102d0: 4a45 4354 2069 7320 6120 706f 6c79 676f JECT is a polygo\n-000102e0: 6e2c 2074 6865 20e2 8098 7377 6565 70e2 n, the ...sweep.\n-000102f0: 8099 2063 6f6e 6e65 6374 7320 4e2b 3120 .. connects N+1 \n-00010300: 7375 6363 6573 7369 7665 2063 6f70 6965 successive copie\n-00010310: 730a 6f66 2074 6865 2063 6c6f 7365 6420 s.of the closed \n-00010320: 706f 6c79 6c69 6e65 2062 6f72 6465 7220 polyline border \n-00010330: 6f66 2074 6865 2070 6f6c 7967 6f6e 2074 of the polygon t\n-00010340: 6f20 666f 726d 2062 6f64 7920 706f 6c79 o form body poly\n-00010350: 676f 6e73 0a65 7861 6374 6c79 2061 7320 gons.exactly as \n-00010360: 7468 6f75 6768 2074 6865 2062 6f72 6465 though the borde\n-00010370: 7220 7765 7265 2061 2073 7765 7074 2070 r were a swept p\n-00010380: 6f6c 796c 696e 6520 6173 2064 6573 6372 olyline as descr\n-00010390: 6962 6564 2069 6e20 2a6e 6f74 650a 5377 ibed in *note.Sw\n-000103a0: 6570 7420 6c69 6e65 733a 3a2e 2020 4966 ept lines::. If\n-000103b0: 2074 6865 7265 2061 7265 206d 2070 6f69 there are m poi\n-000103c0: 6e74 7320 696e 2074 6865 206f 7269 6769 nts in the origi\n-000103d0: 6e61 6c20 706f 6c79 676f 6e2c 2074 6865 nal polygon, the\n-000103e0: 6e20 6d4e 0a62 6f64 7920 706f 6c79 676f n mN.body polygo\n-000103f0: 6e73 2061 7265 2066 6f72 6d65 6420 6279 ns are formed by\n-00010400: 2074 6869 7320 7377 6565 702e 2020 5468 this sweep. Th\n-00010410: 6520 626f 6479 2070 6f6c 7967 6f6e 7320 e body polygons \n-00010420: 666f 726d 2061 6e0a e280 9c65 7874 7275 form an....extru\n-00010430: 7369 6f6e e280 9d20 6f66 2074 6865 2062 sion... of the b\n-00010440: 6f75 6e64 6172 7920 6f66 2074 6865 206f oundary of the o\n-00010450: 7269 6769 6e61 6c20 706f 6c79 676f 6e20 riginal polygon \n-00010460: 7769 7468 2074 776f 2068 6f6c 6573 2061 with two holes a\n-00010470: 740a 7468 6520 6f70 656e 2065 6e64 732e t.the open ends.\n-00010480: 0a0a 2020 2046 696e 616c 6c79 2c20 7468 .. Finally, th\n-00010490: 6520 7377 6565 7020 6164 6473 2074 776f e sweep adds two\n-000104a0: 2063 6f70 6965 7320 6f66 2074 6865 206f copies of the o\n-000104b0: 7269 6769 6e61 6c20 706f 6c79 676f 6e20 riginal polygon \n-000104c0: 746f 2063 6f76 6572 0a74 6865 2068 6f6c to cover.the hol\n-000104d0: 6573 2e20 2057 6520 6361 6c6c 2074 6865 es. We call the\n-000104e0: 7365 2068 6f6c 652d 6669 6c6c 696e 6720 se hole-filling \n-000104f0: 706f 6c79 676f 6e73 20e2 809c 656e 6473 polygons ...ends\n-00010500: e280 9d2e 2020 496e 2074 6869 7320 6d61 .... In this ma\n-00010510: 6e6e 6572 2c0a e280 9873 7765 6570 e280 nner,....sweep..\n-00010520: 9920 666f 726d 7320 7468 6520 626f 756e . forms the boun\n-00010530: 6461 7279 206f 6620 6120 7468 7265 652d dary of a three-\n-00010540: 6469 6d65 6e73 696f 6e61 6c20 6f62 6a65 dimensional obje\n-00010550: 6374 2066 726f 6d20 610a 7477 6f2d 6469 ct from a.two-di\n-00010560: 6d65 6e73 696f 6e61 6c20 706f 6c79 676f mensional polygo\n-00010570: 6e2e 0a0a 2020 2054 6865 206f 7264 6572 n... The order\n-00010580: 206f 6620 7665 7274 6963 6573 206f 6620 of vertices of \n-00010590: 656e 6420 706f 6c79 676f 6e73 2069 7320 end polygons is \n-000105a0: 696d 706f 7274 616e 7420 666f 7220 636f important for co\n-000105b0: 7272 6563 740a 6375 6c6c 696e 6720 6173 rrect.culling as\n-000105c0: 2064 6573 6372 6962 6564 2061 626f 7665 described above\n-000105d0: 2e20 2041 6e20 6578 6163 7420 636f 7079 . An exact copy\n-000105e0: 206f 6620 7468 6520 6f72 6967 696e 616c of the original\n-000105f0: 2070 6f6c 7967 6f6e 2077 6974 680a 7665 polygon with.ve\n-00010600: 7274 6578 206f 7264 6572 2069 6e74 6163 rtex order intac\n-00010610: 7420 666f 726d 7320 7468 6520 6669 7273 t forms the firs\n-00010620: 7420 656e 6420 706f 6c79 676f 6e2e 2020 t end polygon. \n-00010630: 5468 6520 6f74 6865 7220 656e 6420 706f The other end po\n-00010640: 6c79 676f 6e0a 7265 7375 6c74 7320 6672 lygon.results fr\n-00010650: 6f6d 2074 7261 6e73 666f 726d 696e 6720 om transforming \n-00010660: 616e 6420 7468 6520 7265 7665 7273 696e and the reversin\n-00010670: 6720 7468 6520 6f72 6465 7220 6f66 2076 g the order of v\n-00010680: 6572 7469 6365 7320 696e 2074 6865 0a6f ertices in the.o\n-00010690: 7269 6769 6e61 6c2e 2020 5468 6520 7472 riginal. The tr\n-000106a0: 616e 7366 6f72 6d20 706c 6163 6573 2074 ansform places t\n-000106b0: 6865 206f 7269 6769 6e61 6c20 706f 6c79 he original poly\n-000106c0: 676f 6e20 6174 2074 6865 2075 6e63 6f76 gon at the uncov\n-000106d0: 6572 6564 0a68 6f6c 653b 2069 7420 6973 ered.hole; it is\n-000106e0: 0a20 2020 2020 545f 315e 6e20 7468 656e . T_1^n then\n-000106f0: 2054 5f32 5e6e 2074 6865 6e20 2e2e 2e20 T_2^n then ... \n-00010700: 7468 656e 2054 5f52 5e6e 2e0a 4966 2074 then T_R^n..If t\n-00010710: 6865 7265 2061 7265 206e 6f20 6f70 7469 here are no opti\n-00010720: 6f6e 7320 6f6e 2074 6865 2073 7765 7074 ons on the swept\n-00010730: 2070 6f6c 7967 6f6e 2c20 7468 656e 2074 polygon, then t\n-00010740: 6865 20e2 8098 7377 6565 70e2 8099 206f he ...sweep... o\n-00010750: 7074 696f 6e73 0a61 7265 2063 6f70 6965 ptions.are copie\n-00010760: 6420 746f 2065 6163 6820 6f75 7470 7574 d to each output\n-00010770: 2070 6f6c 7967 6f6e 2e20 2049 6620 7468 polygon. If th\n-00010780: 6520 7377 6570 7420 706f 6c79 676f 6e20 e swept polygon \n-00010790: 646f 6573 2068 6176 650a 6f70 7469 6f6e does have.option\n-000107a0: 732c 2074 6865 7365 2061 7265 2063 6f70 s, these are cop\n-000107b0: 6965 6420 746f 2074 6865 2065 6e64 733b ied to the ends;\n-000107c0: 2074 6865 2073 7765 6570 206f 7074 696f the sweep optio\n-000107d0: 6e73 2061 7265 2063 6f70 6965 6420 746f ns are copied to\n-000107e0: 0a74 6865 2062 6f64 7920 706f 6c79 676f .the body polygo\n-000107f0: 6e73 2e20 2049 6e20 7468 6973 206d 616e ns. In this man\n-00010800: 6e65 722c 2062 6f64 7920 616e 6420 656e ner, body and en\n-00010810: 6473 206d 6179 2062 6520 6472 6177 6e20 ds may be drawn \n-00010820: 7769 7468 0a64 6966 6665 7265 6e74 2063 with.different c\n-00010830: 6861 7261 6374 6572 6973 7469 6373 2073 haracteristics s\n-00010840: 7563 6820 6173 20e2 8098 6669 6c6c 636f uch as ...fillco\n-00010850: 6c6f 72e2 8099 2e0a 0a1f 0a46 696c 653a lor........File:\n-00010860: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-00010870: 6f64 653a 2053 7765 7074 2062 6c6f 636b ode: Swept block\n-00010880: 732c 2020 4e65 7874 3a20 5377 6565 7020 s, Next: Sweep \n-00010890: 6661 6365 2073 706c 6974 7469 6e67 2c20 face splitting, \n-000108a0: 2050 7265 763a 2053 7765 7074 2070 6f6c Prev: Swept pol\n-000108b0: 7967 6f6e 732c 2020 5570 3a20 5377 6565 ygons, Up: Swee\n-000108c0: 7073 0a0a 332e 322e 362e 3420 5377 6570 ps..3.2.6.4 Swep\n-000108d0: 7420 626c 6f63 6b73 0a2e 2e2e 2e2e 2e2e t blocks........\n-000108e0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a54 ...............T\n-000108f0: 6865 2073 7765 7074 206f 626a 6563 7420 he swept object \n-00010900: 5357 4550 545f 4f42 4a45 4354 206d 6179 SWEPT_OBJECT may\n-00010910: 2061 6c73 6f20 6265 2061 6e79 2063 6f6c also be any col\n-00010920: 6c65 6374 696f 6e20 6f66 2070 6f6c 796c lection of polyl\n-00010930: 696e 6573 0a61 6e64 2070 6f6c 7967 6f6e ines.and polygon\n-00010940: 732e 2020 5468 6973 206d 6179 2062 6520 s. This may be \n-00010950: 6120 626c 6f63 6b20 636f 6d70 6f73 6564 a block composed\n-00010960: 206f 6620 e280 986c 696e 65e2 8099 2061 of ...line... a\n-00010970: 6e64 2f6f 7220 e280 9870 6f6c 7967 6f6e nd/or ...polygon\n-00010980: e280 990a 636f 6d6d 616e 6473 2069 6e20 ....commands in \n-00010990: 6272 6163 6573 20e2 8098 7b20 7de2 8099 braces ...{ }...\n-000109a0: 2c20 6f72 2069 7420 6d61 7920 6265 2074 , or it may be t\n-000109b0: 6865 2072 6573 756c 7420 6f66 2061 20e2 he result of a .\n-000109c0: 8098 7265 7065 6174 e280 992c 2061 6e6f ..repeat..., ano\n-000109d0: 7468 6572 0ae2 8098 7377 6565 70e2 8099 ther....sweep...\n-000109e0: 2c20 6574 632e 2020 5468 6520 7377 6565 , etc. The swee\n-000109f0: 7020 6163 7473 2069 6e64 6570 656e 6465 p acts independe\n-00010a00: 6e74 6c79 206f 6e20 6561 6368 206f 626a ntly on each obj\n-00010a10: 6563 7420 696e 2074 6865 2062 6c6f 636b ect in the block\n-00010a20: 0a65 7861 6374 6c79 2061 7320 6966 2069 .exactly as if i\n-00010a30: 7420 7765 7265 2061 2073 696e 676c 6520 t were a single \n-00010a40: 7377 6570 7420 6f62 6a65 6374 2064 6573 swept object des\n-00010a50: 6372 6962 6564 2061 626f 7665 2069 6e20 cribed above in \n-00010a60: 2a6e 6f74 650a 5377 6570 7420 6c69 6e65 *note.Swept line\n-00010a70: 733a 3a20 616e 6420 2a6e 6f74 6520 5377 s:: and *note Sw\n-00010a80: 6570 7420 706f 6c79 676f 6e73 3a3a 2e0a ept polygons::..\n-00010a90: 0a1f 0a46 696c 653a 2073 6b65 7463 682e ...File: sketch.\n-00010aa0: 696e 666f 2c20 204e 6f64 653a 2053 7765 info, Node: Swe\n-00010ab0: 6570 2066 6163 6520 7370 6c69 7474 696e ep face splittin\n-00010ac0: 672c 2020 5072 6576 3a20 5377 6570 7420 g, Prev: Swept \n-00010ad0: 626c 6f63 6b73 2c20 2055 703a 2053 7765 blocks, Up: Swe\n-00010ae0: 6570 730a 0a33 2e32 2e36 2e35 2053 7765 eps..3.2.6.5 Swe\n-00010af0: 6570 2066 6163 6520 7370 6c69 7474 696e ep face splittin\n-00010b00: 670a 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e g...............\n-00010b10: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a ................\n-00010b20: 4265 666f 7265 2073 656e 6469 6e67 2065 Before sending e\n-00010b30: 6163 6820 666f 7572 2d73 6964 6564 2062 ach four-sided b\n-00010b40: 6f64 7920 706f 6c79 676f 6e20 6f66 2061 ody polygon of a\n-00010b50: 20e2 8098 7377 6565 70e2 8099 2074 6f20 ...sweep... to \n-00010b60: 7468 6520 6f75 7470 7574 2c0a e280 9873 the output,....s\n-00010b70: 6b65 7463 68e2 8099 2074 6573 7473 2074 ketch... tests t\n-00010b80: 6f20 7365 6520 6966 2069 7420 6973 2072 o see if it is r\n-00010b90: 6f75 6768 6c79 2070 6c61 6e61 722e 2020 oughly planar. \n-00010ba0: 5369 6e63 6520 706c 616e 6172 6974 7920 Since planarity \n-00010bb0: 6973 0a6e 6563 6573 7361 7279 2066 6f72 is.necessary for\n-00010bc0: 2070 726f 7065 7220 6675 6e63 7469 6f6e proper function\n-00010bd0: 696e 6720 6f66 2074 6865 2068 6964 6465 ing of the hidde\n-00010be0: 6e20 7375 7266 6163 6520 616c 676f 7269 n surface algori\n-00010bf0: 7468 6d2c 0a22 7761 7270 6564 2220 706f thm,.\"warped\" po\n-00010c00: 6c79 676f 6e73 2061 7265 2061 7574 6f6d lygons are autom\n-00010c10: 6174 6963 616c 6c79 2073 706c 6974 2069 atically split i\n-00010c20: 6e74 6f20 7477 6f20 7472 6961 6e67 6c65 nto two triangle\n-00010c30: 732e 0a0a 2020 2048 6f6c 652d 6669 6c6c s... Hole-fill\n-00010c40: 696e 6720 706f 6c79 676f 6e73 2070 726f ing polygons pro\n-00010c50: 6475 6365 6420 6279 2063 6c6f 7375 7265 duced by closure\n-00010c60: 2d74 6167 6765 6420 6c69 6e65 2073 7765 -tagged line swe\n-00010c70: 6570 7320 6172 6520 6e6f 740a 7370 6c69 eps are not.spli\n-00010c80: 742e 2020 4e6f 7220 6172 6520 6f72 6967 t. Nor are orig\n-00010c90: 696e 616c 2070 6f6c 7967 6f6e 7320 696e inal polygons in\n-00010ca0: 2070 6f6c 7967 6f6e 2073 7765 6570 732e polygon sweeps.\n-00010cb0: 2020 4974 2069 7320 7468 6520 7573 6572 It is the user\n-00010cc0: 2773 0a72 6573 706f 6e73 6962 696c 6974 's.responsibilit\n-00010cd0: 7920 746f 2065 6e73 7572 6520 7468 6573 y to ensure thes\n-00010ce0: 6520 6172 6520 706c 616e 6172 2e0a 0a1f e are planar....\n-00010cf0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-00010d00: 666f 2c20 204e 6f64 653a 2042 6c6f 636b fo, Node: Block\n-00010d10: 732c 2020 4e65 7874 3a20 5265 7065 6174 s, Next: Repeat\n-00010d20: 732c 2020 5072 6576 3a20 5377 6565 7073 s, Prev: Sweeps\n-00010d30: 2c20 2055 703a 2044 7261 7761 626c 6573 , Up: Drawables\n-00010d40: 0a0a 332e 322e 3720 426c 6f63 6b73 0a2d ..3.2.7 Blocks.-\n-00010d50: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a41 6e79 -----------..Any\n-00010d60: 2073 6571 7565 6e63 6520 6f66 2064 7261 sequence of dra\n-00010d70: 7761 626c 6573 206d 6179 2062 6520 6772 wables may be gr\n-00010d80: 6f75 7065 6420 696e 2061 20e2 809c 626c ouped in a ...bl\n-00010d90: 6f63 6be2 809d 206d 6572 656c 7920 6279 ock... merely by\n-00010da0: 0a65 6e63 6c6f 7369 6e67 2074 6865 6d20 .enclosing them \n-00010db0: 696e 2062 7261 6365 7320 e280 987b 207d in braces ...{ }\n-00010dc0: e280 992e 2020 4120 626c 6f63 6b20 6973 .... A block is\n-00010dd0: 2069 7473 656c 6620 6472 6177 6162 6c65 itself drawable\n-00010de0: 2e20 2041 206b 6579 2075 7365 0a6f 6620 . A key use.of \n-00010df0: 626c 6f63 6b73 2069 7320 746f 2065 7874 blocks is to ext\n-00010e00: 656e 6420 7468 6520 6566 6665 6374 206f end the effect o\n-00010e10: 6620 6120 7369 6e67 6c65 20e2 8098 6465 f a single ...de\n-00010e20: 66e2 8099 2c20 2a6e 6f74 650a 4465 6669 f..., *note.Defi\n-00010e30: 6e69 7469 6f6e 733a 3a2c 20e2 8098 7075 nitions::, ...pu\n-00010e40: 74e2 8099 202a 6e6f 7465 2050 7574 733a t... *note Puts:\n-00010e50: 3a2c 20e2 8098 7377 6565 70e2 8099 202a :, ...sweep... *\n-00010e60: 6e6f 7465 2053 7765 6570 733a 3a2c 206f note Sweeps::, o\n-00010e70: 7220 e280 9872 6570 6561 74e2 8099 0a2a r ...repeat....*\n-00010e80: 6e6f 7465 2052 6570 6561 7473 3a3a 2074 note Repeats:: t\n-00010e90: 6f20 696e 636c 7564 6520 7365 7665 7261 o include severa\n-00010ea0: 6c20 6f62 6a65 6374 7320 7261 7468 6572 l objects rather\n-00010eb0: 2074 6861 6e20 6f6e 652e 0a0a 2020 2044 than one... D\n-00010ec0: 6566 696e 6974 696f 6e73 2028 2a4e 6f74 efinitions (*Not\n-00010ed0: 6520 4465 6669 6e69 7469 6f6e 733a 3a2e e Definitions::.\n-00010ee0: 2920 2069 6e73 6964 6520 6120 626c 6f63 ) inside a bloc\n-00010ef0: 6b20 6861 7665 20e2 809c 6c65 7869 6361 k have ...lexica\n-00010f00: 6c0a 7363 6f70 65e2 809d 2065 7874 656e l.scope... exten\n-00010f10: 6469 6e67 2066 726f 6d20 7468 6520 706c ding from the pl\n-00010f20: 6163 6520 6f66 2064 6566 696e 6974 696f ace of definitio\n-00010f30: 6e20 746f 2074 6865 2065 6e64 206f 6620 n to the end of \n-00010f40: 7468 6520 626c 6f63 6b2e 0a0a 1f0a 4669 the block.....Fi\n-00010f50: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-00010f60: 2020 4e6f 6465 3a20 5265 7065 6174 732c Node: Repeats,\n-00010f70: 2020 4e65 7874 3a20 5075 7473 2c20 2050 Next: Puts, P\n-00010f80: 7265 763a 2042 6c6f 636b 732c 2020 5570 rev: Blocks, Up\n-00010f90: 3a20 4472 6177 6162 6c65 730a 0a33 2e32 : Drawables..3.2\n-00010fa0: 2e38 2052 6570 6561 7473 0a2d 2d2d 2d2d .8 Repeats.-----\n-00010fb0: 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 796e 7461 --------..*Synta\n-00010fc0: 783a 2a0a 2020 2020 2072 6570 6561 7420 x:*. repeat \n-00010fd0: 7b20 4e2c 2054 5f31 2c20 545f 322c 202e { N, T_1, T_2, .\n-00010fe0: 2e2e 2c20 545f 5220 7d20 5245 5045 4154 .., T_R } REPEAT\n-00010ff0: 4544 5f4f 424a 4543 540a 5468 6520 7265 ED_OBJECT.The re\n-00011000: 7065 6174 206d 616b 6573 204e 2074 7261 peat makes N tra\n-00011010: 6e73 666f 726d 6564 2063 6f70 6965 7320 nsformed copies \n-00011020: 6f66 2052 4550 4541 5445 445f 4f42 4a45 of REPEATED_OBJE\n-00011030: 4354 2028 696e 636c 7564 696e 6720 7468 CT (including th\n-00011040: 650a 6f72 6967 696e 616c 292e 2020 5468 e.original). Th\n-00011050: 6520 545f 4920 6172 6520 7472 616e 7366 e T_I are transf\n-00011060: 6f72 6d73 2e20 2054 6865 206b 2774 6820 orms. The k'th \n-00011070: 636f 7079 206f 6620 7468 650a 5245 5045 copy of the.REPE\n-00011080: 4154 4544 5f4f 424a 4543 5420 2866 6f72 ATED_OBJECT (for\n-00011090: 206b 3d30 2c31 2c2e 2e2e 2c6e 2d31 2920 k=0,1,...,n-1) \n-000110a0: 6973 2070 726f 6475 6365 6420 696e 2074 is produced in t\n-000110b0: 6865 2073 616d 6520 6d61 6e6e 6572 2061 he same manner a\n-000110c0: 730a 666f 7220 e280 9873 7765 6570 e280 s.for ...sweep..\n-000110d0: 9973 2064 6573 6372 6962 6564 2069 6e20 .s described in \n-000110e0: 2a6e 6f74 6520 5377 6565 7073 3a3a 2e20 *note Sweeps::. \n-000110f0: 2054 6869 7320 6973 2072 6570 6561 7465 This is repeate\n-00011100: 6420 6865 7265 2028 6e6f 2070 756e 0a69 d here (no pun.i\n-00011110: 6e74 656e 6465 6429 2066 6f72 2063 6f6e ntended) for con\n-00011120: 7665 6e69 656e 6365 2e20 2054 6f20 6d61 venience. To ma\n-00011130: 6b65 2074 6865 206b 2774 6820 636f 7079 ke the k'th copy\n-00011140: 2c20 7468 6520 666f 6c6c 6f77 696e 670a , the following.\n-00011150: 7472 616e 7366 6f72 6d20 6973 2061 7070 transform is app\n-00011160: 6c69 6564 2074 6f20 7468 6520 6f72 6967 lied to the orig\n-00011170: 696e 616c 206f 626a 6563 742e 0a20 2020 inal object.. \n-00011180: 2020 545f 315e 6b20 7468 656e 2054 5f32 T_1^k then T_2\n-00011190: 5e6b 2074 6865 6e20 2e2e 2e20 7468 656e ^k then ... then\n-000111a0: 2054 5f52 5e6b 0a48 6572 6520 545e 6b20 T_R^k.Here T^k \n-000111b0: 6d65 616e 7320 2274 7261 6e73 666f 726d means \"transform\n-000111c0: 2054 2061 7070 6c69 6564 206b 2074 696d T applied k tim\n-000111d0: 6573 2e22 0a0a 1f0a 4669 6c65 3a20 736b es.\"....File: sk\n-000111e0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-000111f0: 3a20 5075 7473 2c20 2050 7265 763a 2052 : Puts, Prev: R\n-00011200: 6570 6561 7473 2c20 2055 703a 2044 7261 epeats, Up: Dra\n-00011210: 7761 626c 6573 0a0a 332e 322e 3920 5075 wables..3.2.9 Pu\n-00011220: 7473 0a2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a ts.----------..*\n-00011230: 5379 6e74 6178 3a2a 0a20 2020 2020 7075 Syntax:*. pu\n-00011240: 7420 7b20 5420 7d20 5055 545f 4f42 4a45 t { T } PUT_OBJE\n-00011250: 4354 0a50 7574 206d 6572 656c 7920 6170 CT.Put merely ap\n-00011260: 706c 6965 7320 7472 616e 7366 6f72 6d20 plies transform \n-00011270: 5420 746f 2074 6865 2064 7261 7761 626c T to the drawabl\n-00011280: 6520 5055 545f 4f42 4a45 4354 2e0a 0a1f e PUT_OBJECT....\n-00011290: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-000112a0: 666f 2c20 204e 6f64 653a 2044 6566 696e fo, Node: Defin\n-000112b0: 6974 696f 6e73 2c20 204e 6578 743a 2047 itions, Next: G\n-000112c0: 6c6f 6261 6c20 656e 7669 726f 6e6d 656e lobal environmen\n-000112d0: 742c 2020 5072 6576 3a20 4472 6177 6162 t, Prev: Drawab\n-000112e0: 6c65 732c 2020 5570 3a20 496e 7075 7420 les, Up: Input \n-000112f0: 6c61 6e67 7561 6765 0a0a 332e 3320 4465 language..3.3 De\n-00011300: 6669 6e69 7469 6f6e 730a 3d3d 3d3d 3d3d finitions.======\n-00011310: 3d3d 3d3d 3d3d 3d3d 3d0a 0a44 6566 696e =========..Defin\n-00011320: 6974 696f 6e73 2067 6976 6520 6e61 6d65 itions give name\n-00011330: 7320 746f 20e2 8098 736b 6574 6368 e280 s to ...sketch..\n-00011340: 9920 6f62 6a65 6374 732e 2020 4465 6669 . objects. Defi\n-00011350: 6e69 7469 6f6e 7320 616c 6f6e 6520 6172 nitions alone ar\n-00011360: 650a 6265 6e69 676e 2e20 2041 20e2 8098 e.benign. A ...\n-00011370: 736b 6574 6368 e280 9920 696e 7075 7420 sketch... input \n-00011380: 6669 6c65 2063 6f6e 7369 7374 696e 6720 file consisting \n-00011390: 656e 7469 7265 6c79 206f 6620 6465 6669 entirely of defi\n-000113a0: 6e69 7469 6f6e 7320 7769 6c6c 0a67 656e nitions will.gen\n-000113b0: 6572 6174 6520 6e6f 2064 7261 7769 6e67 erate no drawing\n-000113c0: 2e20 204f 6e6c 7920 7768 656e 2064 6566 . Only when def\n-000113d0: 696e 6974 696f 6e73 2061 7265 20e2 809c initions are ...\n-000113e0: 7265 6665 7265 6e63 6564 e280 9d20 646f referenced... do\n-000113f0: 2074 6865 790a 706f 7465 6e74 6961 6c6c they.potentiall\n-00011400: 7920 6c65 6164 2074 6f20 696e 6b20 6f6e y lead to ink on\n-00011410: 2074 6865 2064 7261 7769 6e67 2e0a 0a20 the drawing... \n-00011420: 2020 5468 6520 696e 7465 6e74 206f 6620 The intent of \n-00011430: 6465 6669 6e69 7469 6f6e 7320 6973 2074 definitions is t\n-00011440: 6f20 6d61 6b65 20e2 8098 736b 6574 6368 o make ...sketch\n-00011450: e280 9920 636f 6465 206d 6f72 6520 636f ... code more co\n-00011460: 6e63 6973 6520 616e 640a 7265 6164 6162 ncise and.readab\n-00011470: 6c65 2e20 2054 6865 7265 2069 7320 6e6f le. There is no\n-00011480: 2069 6e70 7574 2066 696c 6520 656d 706c input file empl\n-00011490: 6f79 696e 6720 6465 6669 6e69 7469 6f6e oying definition\n-000114a0: 7320 7468 6174 2063 6f75 6c64 206e 6f74 s that could not\n-000114b0: 0a62 6520 7265 2d77 7269 7474 656e 2077 .be re-written w\n-000114c0: 6974 686f 7574 2074 6865 6d2e 0a0a 2020 ithout them... \n-000114d0: 2044 6566 696e 6162 6c65 206f 626a 6563 Definable objec\n-000114e0: 7473 2069 6e63 6c75 6465 2061 6e79 2072 ts include any r\n-000114f0: 6573 756c 7420 6f66 2061 6e20 6166 6669 esult of an affi\n-00011500: 6e65 2061 7269 7468 6d65 7469 630a 6578 ne arithmetic.ex\n-00011510: 7072 6573 7369 6f6e 2028 7363 616c 6172 pression (scalar\n-00011520: 2c20 706f 696e 742c 2076 6563 746f 722c , point, vector,\n-00011530: 206f 7220 7472 616e 7366 6f72 6d29 2c20 or transform), \n-00011540: 616e 7920 6472 6177 6162 6c65 206f 626a any drawable obj\n-00011550: 6563 740a 2864 6f74 732c 206c 696e 652c ect.(dots, line,\n-00011560: 2063 7572 7665 2c20 706f 6c79 676f 6e2c curve, polygon,\n-00011570: 2062 6c6f 636b 2c20 7377 6565 702c 2070 block, sweep, p\n-00011580: 7574 2c20 7265 7065 6174 2c20 6f72 2073 ut, repeat, or s\n-00011590: 7065 6369 616c 292c 2061 6e64 0a6f 7074 pecial), and.opt\n-000115a0: 696f 6e20 7374 7269 6e67 732e 2020 496e ion strings. In\n-000115b0: 2061 6464 6974 696f 6e2c 20e2 809c 7461 addition, ...ta\n-000115c0: 6720 6465 6669 6e69 7469 6f6e 73e2 809d g definitions...\n-000115d0: 2c20 7768 6963 6820 6861 7665 206e 6f0a , which have no.\n-000115e0: 6173 736f 6369 6174 6564 206f 626a 6563 associated objec\n-000115f0: 7420 6174 2061 6c6c 2c20 616c 6c6f 7720 t at all, allow \n-00011600: 7468 6520 6d65 616e 696e 6720 6f66 206f the meaning of o\n-00011610: 7468 6572 2064 6566 696e 6974 696f 6e73 ther definitions\n-00011620: 2074 6f20 6265 0a73 656c 6563 7465 6420 to be.selected \n-00011630: 6672 6f6d 2061 2073 6574 206f 6620 616c from a set of al\n-00011640: 7465 726e 6174 6976 6573 2e20 2053 696e ternatives. Sin\n-00011650: 6365 2074 6167 7320 6d61 7920 6265 2064 ce tags may be d\n-00011660: 6566 696e 6564 2028 616e 640a 756e 6465 efined (and.unde\n-00011670: 6669 6e65 6429 2069 6e20 7468 6520 636f fined) in the co\n-00011680: 6d6d 616e 6420 6c69 6e65 206f 6620 e280 mmand line of ..\n-00011690: 9873 6b65 7463 68e2 8099 2c20 7468 6579 .sketch..., they\n-000116a0: 2063 616e 2062 6520 616e 2061 6964 2069 can be an aid i\n-000116b0: 6e20 7468 650a 7363 7269 7074 2d64 7269 n the.script-dri\n-000116c0: 7665 6e20 7072 6570 6172 6174 696f 6e20 ven preparation \n-000116d0: 6f66 2064 6f63 756d 656e 7473 2e0a 0a2a of documents...*\n-000116e0: 204d 656e 753a 0a0a 2a20 466f 726d 7320 Menu:..* Forms \n-000116f0: 6f66 2064 6566 696e 6974 696f 6e73 3a3a of definitions::\n-00011700: 2020 2020 2020 2020 4469 6666 6572 656e Differen\n-00011710: 7420 6465 6673 2066 6f72 2064 6966 6665 t defs for diffe\n-00011720: 7265 6e74 2070 7572 706f 7365 732e 0a2a rent purposes..*\n-00011730: 2046 6f72 6d73 206f 6620 7265 6665 7265 Forms of refere\n-00011740: 6e63 6573 3a3a 2020 2020 2020 2020 2048 nces:: H\n-00011750: 6f77 2072 6566 6572 656e 6365 7320 6465 ow references de\n-00011760: 6e6f 7465 2074 7970 6573 2e0a 0a1f 0a46 note types.....F\n-00011770: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n-00011780: 2c20 204e 6f64 653a 2046 6f72 6d73 206f , Node: Forms o\n-00011790: 6620 6465 6669 6e69 7469 6f6e 732c 2020 f definitions, \n-000117a0: 4e65 7874 3a20 466f 726d 7320 6f66 2072 Next: Forms of r\n-000117b0: 6566 6572 656e 6365 732c 2020 5072 6576 eferences, Prev\n-000117c0: 3a20 4465 6669 6e69 7469 6f6e 732c 2020 : Definitions, \n-000117d0: 5570 3a20 4465 6669 6e69 7469 6f6e 730a Up: Definitions.\n-000117e0: 0a33 2e33 2e31 2046 6f72 6d73 206f 6620 .3.3.1 Forms of \n-000117f0: 6465 6669 6e69 7469 6f6e 730a 2d2d 2d2d definitions.----\n+000102c0: 2e0a 0a49 6620 5357 4550 545f 4f42 4a45 ...If SWEPT_OBJE\n+000102d0: 4354 2069 7320 6120 706f 6c79 676f 6e2c CT is a polygon,\n+000102e0: 2074 6865 20e2 8098 7377 6565 70e2 8099 the ...sweep...\n+000102f0: 2063 6f6e 6e65 6374 7320 4e2b 3120 7375 connects N+1 su\n+00010300: 6363 6573 7369 7665 2063 6f70 6965 730a ccessive copies.\n+00010310: 6f66 2074 6865 2063 6c6f 7365 6420 706f of the closed po\n+00010320: 6c79 6c69 6e65 2062 6f72 6465 7220 6f66 lyline border of\n+00010330: 2074 6865 2070 6f6c 7967 6f6e 2074 6f20 the polygon to \n+00010340: 666f 726d 2062 6f64 7920 706f 6c79 676f form body polygo\n+00010350: 6e73 0a65 7861 6374 6c79 2061 7320 7468 ns.exactly as th\n+00010360: 6f75 6768 2074 6865 2062 6f72 6465 7220 ough the border \n+00010370: 7765 7265 2061 2073 7765 7074 2070 6f6c were a swept pol\n+00010380: 796c 696e 6520 6173 2064 6573 6372 6962 yline as describ\n+00010390: 6564 2069 6e20 2a6e 6f74 650a 5377 6570 ed in *note.Swep\n+000103a0: 7420 6c69 6e65 733a 3a2e 2020 4966 2074 t lines::. If t\n+000103b0: 6865 7265 2061 7265 206d 2070 6f69 6e74 here are m point\n+000103c0: 7320 696e 2074 6865 206f 7269 6769 6e61 s in the origina\n+000103d0: 6c20 706f 6c79 676f 6e2c 2074 6865 6e20 l polygon, then \n+000103e0: 6d4e 0a62 6f64 7920 706f 6c79 676f 6e73 mN.body polygons\n+000103f0: 2061 7265 2066 6f72 6d65 6420 6279 2074 are formed by t\n+00010400: 6869 7320 7377 6565 702e 2020 5468 6520 his sweep. The \n+00010410: 626f 6479 2070 6f6c 7967 6f6e 7320 666f body polygons fo\n+00010420: 726d 2061 6e0a e280 9c65 7874 7275 7369 rm an....extrusi\n+00010430: 6f6e e280 9d20 6f66 2074 6865 2062 6f75 on... of the bou\n+00010440: 6e64 6172 7920 6f66 2074 6865 206f 7269 ndary of the ori\n+00010450: 6769 6e61 6c20 706f 6c79 676f 6e20 7769 ginal polygon wi\n+00010460: 7468 2074 776f 2068 6f6c 6573 2061 740a th two holes at.\n+00010470: 7468 6520 6f70 656e 2065 6e64 732e 0a0a the open ends...\n+00010480: 2020 2046 696e 616c 6c79 2c20 7468 6520 Finally, the \n+00010490: 7377 6565 7020 6164 6473 2074 776f 2063 sweep adds two c\n+000104a0: 6f70 6965 7320 6f66 2074 6865 206f 7269 opies of the ori\n+000104b0: 6769 6e61 6c20 706f 6c79 676f 6e20 746f ginal polygon to\n+000104c0: 2063 6f76 6572 0a74 6865 2068 6f6c 6573 cover.the holes\n+000104d0: 2e20 2057 6520 6361 6c6c 2074 6865 7365 . We call these\n+000104e0: 2068 6f6c 652d 6669 6c6c 696e 6720 706f hole-filling po\n+000104f0: 6c79 676f 6e73 20e2 809c 656e 6473 e280 lygons ...ends..\n+00010500: 9d2e 2020 496e 2074 6869 7320 6d61 6e6e .. In this mann\n+00010510: 6572 2c0a e280 9873 7765 6570 e280 9920 er,....sweep... \n+00010520: 666f 726d 7320 7468 6520 626f 756e 6461 forms the bounda\n+00010530: 7279 206f 6620 6120 7468 7265 652d 6469 ry of a three-di\n+00010540: 6d65 6e73 696f 6e61 6c20 6f62 6a65 6374 mensional object\n+00010550: 2066 726f 6d20 610a 7477 6f2d 6469 6d65 from a.two-dime\n+00010560: 6e73 696f 6e61 6c20 706f 6c79 676f 6e2e nsional polygon.\n+00010570: 0a0a 2020 2054 6865 206f 7264 6572 206f .. The order o\n+00010580: 6620 7665 7274 6963 6573 206f 6620 656e f vertices of en\n+00010590: 6420 706f 6c79 676f 6e73 2069 7320 696d d polygons is im\n+000105a0: 706f 7274 616e 7420 666f 7220 636f 7272 portant for corr\n+000105b0: 6563 740a 6375 6c6c 696e 6720 6173 2064 ect.culling as d\n+000105c0: 6573 6372 6962 6564 2061 626f 7665 2e20 escribed above. \n+000105d0: 2041 6e20 6578 6163 7420 636f 7079 206f An exact copy o\n+000105e0: 6620 7468 6520 6f72 6967 696e 616c 2070 f the original p\n+000105f0: 6f6c 7967 6f6e 2077 6974 680a 7665 7274 olygon with.vert\n+00010600: 6578 206f 7264 6572 2069 6e74 6163 7420 ex order intact \n+00010610: 666f 726d 7320 7468 6520 6669 7273 7420 forms the first \n+00010620: 656e 6420 706f 6c79 676f 6e2e 2020 5468 end polygon. Th\n+00010630: 6520 6f74 6865 7220 656e 6420 706f 6c79 e other end poly\n+00010640: 676f 6e0a 7265 7375 6c74 7320 6672 6f6d gon.results from\n+00010650: 2074 7261 6e73 666f 726d 696e 6720 616e transforming an\n+00010660: 6420 7468 6520 7265 7665 7273 696e 6720 d the reversing \n+00010670: 7468 6520 6f72 6465 7220 6f66 2076 6572 the order of ver\n+00010680: 7469 6365 7320 696e 2074 6865 0a6f 7269 tices in the.ori\n+00010690: 6769 6e61 6c2e 2020 5468 6520 7472 616e ginal. The tran\n+000106a0: 7366 6f72 6d20 706c 6163 6573 2074 6865 sform places the\n+000106b0: 206f 7269 6769 6e61 6c20 706f 6c79 676f original polygo\n+000106c0: 6e20 6174 2074 6865 2075 6e63 6f76 6572 n at the uncover\n+000106d0: 6564 0a68 6f6c 653b 2069 7420 6973 0a20 ed.hole; it is. \n+000106e0: 2020 2020 545f 315e 6e20 7468 656e 2054 T_1^n then T\n+000106f0: 5f32 5e6e 2074 6865 6e20 2e2e 2e20 7468 _2^n then ... th\n+00010700: 656e 2054 5f52 5e6e 2e0a 4966 2074 6865 en T_R^n..If the\n+00010710: 7265 2061 7265 206e 6f20 6f70 7469 6f6e re are no option\n+00010720: 7320 6f6e 2074 6865 2073 7765 7074 2070 s on the swept p\n+00010730: 6f6c 7967 6f6e 2c20 7468 656e 2074 6865 olygon, then the\n+00010740: 20e2 8098 7377 6565 70e2 8099 206f 7074 ...sweep... opt\n+00010750: 696f 6e73 0a61 7265 2063 6f70 6965 6420 ions.are copied \n+00010760: 746f 2065 6163 6820 6f75 7470 7574 2070 to each output p\n+00010770: 6f6c 7967 6f6e 2e20 2049 6620 7468 6520 olygon. If the \n+00010780: 7377 6570 7420 706f 6c79 676f 6e20 646f swept polygon do\n+00010790: 6573 2068 6176 650a 6f70 7469 6f6e 732c es have.options,\n+000107a0: 2074 6865 7365 2061 7265 2063 6f70 6965 these are copie\n+000107b0: 6420 746f 2074 6865 2065 6e64 733b 2074 d to the ends; t\n+000107c0: 6865 2073 7765 6570 206f 7074 696f 6e73 he sweep options\n+000107d0: 2061 7265 2063 6f70 6965 6420 746f 0a74 are copied to.t\n+000107e0: 6865 2062 6f64 7920 706f 6c79 676f 6e73 he body polygons\n+000107f0: 2e20 2049 6e20 7468 6973 206d 616e 6e65 . In this manne\n+00010800: 722c 2062 6f64 7920 616e 6420 656e 6473 r, body and ends\n+00010810: 206d 6179 2062 6520 6472 6177 6e20 7769 may be drawn wi\n+00010820: 7468 0a64 6966 6665 7265 6e74 2063 6861 th.different cha\n+00010830: 7261 6374 6572 6973 7469 6373 2073 7563 racteristics suc\n+00010840: 6820 6173 20e2 8098 6669 6c6c 636f 6c6f h as ...fillcolo\n+00010850: 72e2 8099 2e0a 0a1f 0a46 696c 653a 2073 r........File: s\n+00010860: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+00010870: 653a 2053 7765 7074 2062 6c6f 636b 732c e: Swept blocks,\n+00010880: 2020 4e65 7874 3a20 5377 6565 7020 6661 Next: Sweep fa\n+00010890: 6365 2073 706c 6974 7469 6e67 2c20 2050 ce splitting, P\n+000108a0: 7265 763a 2053 7765 7074 2070 6f6c 7967 rev: Swept polyg\n+000108b0: 6f6e 732c 2020 5570 3a20 5377 6565 7073 ons, Up: Sweeps\n+000108c0: 0a0a 332e 322e 362e 3420 5377 6570 7420 ..3.2.6.4 Swept \n+000108d0: 626c 6f63 6b73 0a2e 2e2e 2e2e 2e2e 2e2e blocks..........\n+000108e0: 2e2e 2e2e 2e2e 2e2e 2e2e 2e0a 0a54 6865 .............The\n+000108f0: 2073 7765 7074 206f 626a 6563 7420 5357 swept object SW\n+00010900: 4550 545f 4f42 4a45 4354 206d 6179 2061 EPT_OBJECT may a\n+00010910: 6c73 6f20 6265 2061 6e79 2063 6f6c 6c65 lso be any colle\n+00010920: 6374 696f 6e20 6f66 2070 6f6c 796c 696e ction of polylin\n+00010930: 6573 0a61 6e64 2070 6f6c 7967 6f6e 732e es.and polygons.\n+00010940: 2020 5468 6973 206d 6179 2062 6520 6120 This may be a \n+00010950: 626c 6f63 6b20 636f 6d70 6f73 6564 206f block composed o\n+00010960: 6620 e280 986c 696e 65e2 8099 2061 6e64 f ...line... and\n+00010970: 2f6f 7220 e280 9870 6f6c 7967 6f6e e280 /or ...polygon..\n+00010980: 990a 636f 6d6d 616e 6473 2069 6e20 6272 ..commands in br\n+00010990: 6163 6573 20e2 8098 7b20 7de2 8099 2c20 aces ...{ }..., \n+000109a0: 6f72 2069 7420 6d61 7920 6265 2074 6865 or it may be the\n+000109b0: 2072 6573 756c 7420 6f66 2061 20e2 8098 result of a ...\n+000109c0: 7265 7065 6174 e280 992c 2061 6e6f 7468 repeat..., anoth\n+000109d0: 6572 0ae2 8098 7377 6565 70e2 8099 2c20 er....sweep..., \n+000109e0: 6574 632e 2020 5468 6520 7377 6565 7020 etc. The sweep \n+000109f0: 6163 7473 2069 6e64 6570 656e 6465 6e74 acts independent\n+00010a00: 6c79 206f 6e20 6561 6368 206f 626a 6563 ly on each objec\n+00010a10: 7420 696e 2074 6865 2062 6c6f 636b 0a65 t in the block.e\n+00010a20: 7861 6374 6c79 2061 7320 6966 2069 7420 xactly as if it \n+00010a30: 7765 7265 2061 2073 696e 676c 6520 7377 were a single sw\n+00010a40: 6570 7420 6f62 6a65 6374 2064 6573 6372 ept object descr\n+00010a50: 6962 6564 2061 626f 7665 2069 6e20 2a6e ibed above in *n\n+00010a60: 6f74 650a 5377 6570 7420 6c69 6e65 733a ote.Swept lines:\n+00010a70: 3a20 616e 6420 2a6e 6f74 6520 5377 6570 : and *note Swep\n+00010a80: 7420 706f 6c79 676f 6e73 3a3a 2e0a 0a1f t polygons::....\n+00010a90: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n+00010aa0: 666f 2c20 204e 6f64 653a 2053 7765 6570 fo, Node: Sweep\n+00010ab0: 2066 6163 6520 7370 6c69 7474 696e 672c face splitting,\n+00010ac0: 2020 5072 6576 3a20 5377 6570 7420 626c Prev: Swept bl\n+00010ad0: 6f63 6b73 2c20 2055 703a 2053 7765 6570 ocks, Up: Sweep\n+00010ae0: 730a 0a33 2e32 2e36 2e35 2053 7765 6570 s..3.2.6.5 Sweep\n+00010af0: 2066 6163 6520 7370 6c69 7474 696e 670a face splitting.\n+00010b00: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n+00010b10: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 0a0a 4265 ..............Be\n+00010b20: 666f 7265 2073 656e 6469 6e67 2065 6163 fore sending eac\n+00010b30: 6820 666f 7572 2d73 6964 6564 2062 6f64 h four-sided bod\n+00010b40: 7920 706f 6c79 676f 6e20 6f66 2061 20e2 y polygon of a .\n+00010b50: 8098 7377 6565 70e2 8099 2074 6f20 7468 ..sweep... to th\n+00010b60: 6520 6f75 7470 7574 2c0a e280 9873 6b65 e output,....ske\n+00010b70: 7463 68e2 8099 2074 6573 7473 2074 6f20 tch... tests to \n+00010b80: 7365 6520 6966 2069 7420 6973 2072 6f75 see if it is rou\n+00010b90: 6768 6c79 2070 6c61 6e61 722e 2020 5369 ghly planar. Si\n+00010ba0: 6e63 6520 706c 616e 6172 6974 7920 6973 nce planarity is\n+00010bb0: 0a6e 6563 6573 7361 7279 2066 6f72 2070 .necessary for p\n+00010bc0: 726f 7065 7220 6675 6e63 7469 6f6e 696e roper functionin\n+00010bd0: 6720 6f66 2074 6865 2068 6964 6465 6e20 g of the hidden \n+00010be0: 7375 7266 6163 6520 616c 676f 7269 7468 surface algorith\n+00010bf0: 6d2c 0a22 7761 7270 6564 2220 706f 6c79 m,.\"warped\" poly\n+00010c00: 676f 6e73 2061 7265 2061 7574 6f6d 6174 gons are automat\n+00010c10: 6963 616c 6c79 2073 706c 6974 2069 6e74 ically split int\n+00010c20: 6f20 7477 6f20 7472 6961 6e67 6c65 732e o two triangles.\n+00010c30: 0a0a 2020 2048 6f6c 652d 6669 6c6c 696e .. Hole-fillin\n+00010c40: 6720 706f 6c79 676f 6e73 2070 726f 6475 g polygons produ\n+00010c50: 6365 6420 6279 2063 6c6f 7375 7265 2d74 ced by closure-t\n+00010c60: 6167 6765 6420 6c69 6e65 2073 7765 6570 agged line sweep\n+00010c70: 7320 6172 6520 6e6f 740a 7370 6c69 742e s are not.split.\n+00010c80: 2020 4e6f 7220 6172 6520 6f72 6967 696e Nor are origin\n+00010c90: 616c 2070 6f6c 7967 6f6e 7320 696e 2070 al polygons in p\n+00010ca0: 6f6c 7967 6f6e 2073 7765 6570 732e 2020 olygon sweeps. \n+00010cb0: 4974 2069 7320 7468 6520 7573 6572 2773 It is the user's\n+00010cc0: 0a72 6573 706f 6e73 6962 696c 6974 7920 .responsibility \n+00010cd0: 746f 2065 6e73 7572 6520 7468 6573 6520 to ensure these \n+00010ce0: 6172 6520 706c 616e 6172 2e0a 0a1f 0a46 are planar.....F\n+00010cf0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+00010d00: 2c20 204e 6f64 653a 2042 6c6f 636b 732c , Node: Blocks,\n+00010d10: 2020 4e65 7874 3a20 5265 7065 6174 732c Next: Repeats,\n+00010d20: 2020 5072 6576 3a20 5377 6565 7073 2c20 Prev: Sweeps, \n+00010d30: 2055 703a 2044 7261 7761 626c 6573 0a0a Up: Drawables..\n+00010d40: 332e 322e 3720 426c 6f63 6b73 0a2d 2d2d 3.2.7 Blocks.---\n+00010d50: 2d2d 2d2d 2d2d 2d2d 2d0a 0a41 6e79 2073 ---------..Any s\n+00010d60: 6571 7565 6e63 6520 6f66 2064 7261 7761 equence of drawa\n+00010d70: 626c 6573 206d 6179 2062 6520 6772 6f75 bles may be grou\n+00010d80: 7065 6420 696e 2061 20e2 809c 626c 6f63 ped in a ...bloc\n+00010d90: 6be2 809d 206d 6572 656c 7920 6279 0a65 k... merely by.e\n+00010da0: 6e63 6c6f 7369 6e67 2074 6865 6d20 696e nclosing them in\n+00010db0: 2062 7261 6365 7320 e280 987b 207d e280 braces ...{ }..\n+00010dc0: 992e 2020 4120 626c 6f63 6b20 6973 2069 .. 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(\n-000124b0: 6275 7420 6e6f 7420 e280 986c 6179 e280 but not ...lay..\n-000124c0: 9929 2e20 202a 4e6f 7465 2049 6e74 6572 .). *Note Inter\n-000124d0: 6e61 6c20 6f70 7469 6f6e 733a 3a2e 0a0a nal options::...\n-000124e0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n-000124f0: 6e66 6f2c 2020 4e6f 6465 3a20 4361 6d65 nfo, Node: Came\n-00012500: 7261 2c20 204e 6578 743a 2050 6963 7475 ra, Next: Pictu\n-00012510: 7265 2062 6f78 2c20 2050 7265 763a 2047 re box, Prev: G\n-00012520: 6c6f 6261 6c20 6f70 7469 6f6e 732c 2020 lobal options, \n-00012530: 5570 3a20 476c 6f62 616c 2065 6e76 6972 Up: Global envir\n-00012540: 6f6e 6d65 6e74 0a0a 332e 342e 3220 4361 onment..3.4.2 Ca\n-00012550: 6d65 7261 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d mera.-----------\n-00012560: 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 2020 -..*Syntax:*. \n-00012570: 2020 6361 6d65 7261 2054 5241 4e53 464f camera TRANSFO\n-00012580: 524d 5f45 5850 5245 5353 494f 4e0a 2020 RM_EXPRESSION. \n-00012590: 2054 6865 2054 5241 4e53 464f 524d 5f45 The TRANSFORM_E\n-000125a0: 5850 5245 5353 494f 4e20 6973 2061 7070 XPRESSION is app\n-000125b0: 6c69 6564 2061 6674 6572 2061 6c6c 206f lied after all o\n-000125c0: 7468 6572 2074 7261 6e73 666f 726d 6174 ther transformat\n-000125d0: 696f 6e73 0a6f 6620 7468 6520 7363 656e ions.of the scen\n-000125e0: 652e 2020 5468 6973 2069 7320 6375 7272 e. This is curr\n-000125f0: 656e 746c 7920 6f6e 6c79 2075 7365 6675 ently only usefu\n-00012600: 6c20 666f 7220 7472 616e 7366 6f72 6d69 l for transformi\n-00012610: 6e67 2074 6865 0a62 6f75 6e64 696e 6720 ng the.bounding \n-00012620: 626f 782e 2020 2a4e 6f74 6520 5069 6374 box. *Note Pict\n-00012630: 7572 6520 626f 783a 3a2e 2020 4974 2077 ure box::. It w\n-00012640: 696c 6c20 706c 6179 2061 2072 6f6c 6520 ill play a role \n-00012650: 696e 2061 6e79 2066 7574 7572 650a 696d in any future.im\n-00012660: 706c 656d 656e 7461 7469 6f6e 206f 6620 plementation of \n-00012670: 636c 6970 7069 6e67 2e0a 0a1f 0a46 696c clipping.....Fil\n-00012680: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-00012690: 204e 6f64 653a 2050 6963 7475 7265 2062 Node: Picture b\n-000126a0: 6f78 2c20 204e 6578 743a 2046 7261 6d65 ox, Next: Frame\n-000126b0: 2c20 2050 7265 763a 2043 616d 6572 612c , Prev: Camera,\n-000126c0: 2020 5570 3a20 476c 6f62 616c 2065 6e76 Up: Global env\n-000126d0: 6972 6f6e 6d65 6e74 0a0a 332e 342e 3320 ironment..3.4.3 \n-000126e0: 5069 6374 7572 6520 626f 780a 2d2d 2d2d Picture box.----\n-000126f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a -------------..*\n-00012700: 5379 6e74 6178 3a2a 0a20 2020 2020 7069 Syntax:*. pi\n-00012710: 6374 7572 6562 6f78 5b42 4153 454c 494e cturebox[BASELIN\n-00012720: 455d 0a20 2020 2020 7069 6374 7572 6562 E]. pictureb\n-00012730: 6f78 5b42 4153 454c 494e 455d 2028 5031 ox[BASELINE] (P1\n-00012740: 2928 5032 290a 5468 6520 6669 7273 7420 )(P2).The first \n-00012750: 666f 726d 206f 6620 e280 9870 6963 7475 form of ...pictu\n-00012760: 7265 626f 78e2 8099 2063 6175 7365 7320 rebox... causes \n-00012770: 6120 7363 616c 6172 2042 4153 454c 494e a scalar BASELIN\n-00012780: 4520 6672 6163 7469 6f6e 2074 6f20 6265 E fraction to be\n-00012790: 0a65 6d69 7474 6564 2069 6e20 7468 6520 .emitted in the \n-000127a0: e280 9870 7370 6963 7475 7265 e280 9920 ...pspicture... \n-000127b0: 656e 7669 726f 6e6d 656e 7420 6f66 2074 environment of t\n-000127c0: 6865 206f 7574 7075 742e 2020 5365 6520 he output. See \n-000127d0: e280 9850 5354 7269 636b 73e2 8099 0a64 ...PSTricks....d\n-000127e0: 6f63 756d 656e 7461 7469 6f6e 2066 6f72 ocumentation for\n-000127f0: 20e2 8098 7073 7069 6374 7572 65e2 8099 ...pspicture...\n-00012800: 2e0a 0a20 2020 496e 2074 6865 2073 6563 ... In the sec\n-00012810: 6f6e 6420 666f 726d 2c20 7468 6520 4241 ond form, the BA\n-00012820: 5345 4c49 4e45 2066 7261 6374 696f 6e20 SELINE fraction \n-00012830: 6973 206f 7074 696f 6e61 6c2c 2061 6e64 is optional, and\n-00012840: 2074 6865 2074 776f 0a70 6f69 6e74 7320 the two.points \n-00012850: 7468 6174 2066 6f6c 6c6f 7720 6465 6669 that follow defi\n-00012860: 6e65 2074 6865 2064 6961 676f 6e61 6c20 ne the diagonal \n-00012870: 6f66 2061 2074 6872 6565 2d64 696d 656e of a three-dimen\n-00012880: 7369 6f6e 616c 2062 6f75 6e64 696e 670a sional bounding.\n-00012890: 626f 7820 666f 7220 7468 6520 636f 6d70 box for the comp\n-000128a0: 6c65 7465 6420 7363 656e 652e 2020 5468 leted scene. Th\n-000128b0: 6520 7061 7261 6c6c 656c 2070 726f 6a65 e parallel proje\n-000128c0: 6374 696f 6e20 6f66 2074 6865 2062 6f75 ction of the bou\n-000128d0: 6e64 696e 670a 626f 7820 6465 7465 726d nding.box determ\n-000128e0: 696e 6573 2074 6865 2063 6f72 6e65 7273 ines the corners\n-000128f0: 206f 6620 7468 6520 6472 6177 696e 6727 of the drawing'\n-00012900: 7320 e280 9870 7370 6963 7475 7265 2ae2 s ...pspicture*.\n-00012910: 8099 2065 6e76 6972 6f6e 6d65 6e74 2c0a .. environment,.\n-00012920: 7768 6963 6820 6973 2075 7365 6420 696e which is used in\n-00012930: 2070 6c61 6365 206f 6620 e280 9870 7370 place of ...psp\n-00012940: 6963 7475 7265 e280 992e 2020 5468 6973 icture.... This\n-00012950: 2063 6175 7365 7320 506f 7374 5363 7269 causes PostScri\n-00012960: 7074 2074 6f20 636c 6970 0a74 6865 2066 pt to clip.the f\n-00012970: 696e 616c 2064 7261 7769 6e67 2074 6f20 inal drawing to \n-00012980: 7468 6520 626f 756e 6469 6e67 2062 6f78 the bounding box\n-00012990: 2069 6e20 3264 2e20 2049 6620 7468 6572 in 2d. If ther\n-000129a0: 6520 6973 2061 20e2 8098 6361 6d65 7261 e is a ...camera\n-000129b0: e280 990a 7370 6563 6966 6965 642c 2074 ....specified, t\n-000129c0: 6865 2063 616d 6572 6120 7472 616e 666f he camera tranfo\n-000129d0: 726d 6174 696f 6e20 6973 2061 7070 6c69 rmation is appli\n-000129e0: 6564 2074 6f20 7468 6520 626f 756e 6469 ed to the boundi\n-000129f0: 6e67 2062 6f78 2c20 616e 640a 7468 6520 ng box, and.the \n-00012a00: e280 9870 7370 6963 7475 7265 e280 9920 ...pspicture... \n-00012a10: 6973 2073 6574 206a 7573 7420 6c61 7267 is set just larg\n-00012a20: 6520 656e 6f75 6768 2074 6f20 696e 636c e enough to incl\n-00012a30: 7564 6520 7468 6520 7472 616e 7366 6f72 ude the transfor\n-00012a40: 6d65 6420 626f 782e 0a0a 2020 2057 6865 med box... Whe\n-00012a50: 6e20 6e6f 2062 6f75 6e64 696e 6720 626f n no bounding bo\n-00012a60: 7820 6973 2067 6976 656e 2c20 e280 9873 x is given, ...s\n-00012a70: 6b65 7463 68e2 8099 2063 6f6d 7075 7465 ketch... compute\n-00012a80: 7320 6f6e 6520 6175 746f 6d61 7469 6361 s one automatica\n-00012a90: 6c6c 792e 0a0a 1f0a 4669 6c65 3a20 736b lly.....File: sk\n-00012aa0: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-00012ab0: 3a20 4672 616d 652c 2020 4e65 7874 3a20 : Frame, Next: \n-00012ac0: 4c61 6e67 7561 6765 2c20 2050 7265 763a Language, Prev:\n-00012ad0: 2050 6963 7475 7265 2062 6f78 2c20 2055 Picture box, U\n-00012ae0: 703a 2047 6c6f 6261 6c20 656e 7669 726f p: Global enviro\n-00012af0: 6e6d 656e 740a 0a33 2e34 2e34 2046 7261 nment..3.4.4 Fra\n-00012b00: 6d65 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a me.-----------..\n-00012b10: 2a53 796e 7461 783a 2a0a 2020 2020 2066 *Syntax:*. f\n-00012b20: 7261 6d65 205b 4f50 5449 4f4e 535d 0a43 rame [OPTIONS].C\n-00012b30: 6175 7365 7320 6120 5c70 7366 7261 6d65 auses a \\psframe\n-00012b40: 626f 7820 746f 2073 7572 726f 756e 6420 box to surround \n-00012b50: 7468 6520 e280 9870 7370 6963 7475 7265 the ...pspicture\n-00012b60: e280 9920 656e 7669 726f 6e6d 656e 7420 ... environment \n-00012b70: 696e 2074 6865 0a6f 7574 7075 742e 2020 in the.output. \n-00012b80: 4966 204f 5054 494f 4e53 2061 7265 2070 If OPTIONS are p\n-00012b90: 7265 7365 6e74 2c20 7468 6579 2061 7265 resent, they are\n-00012ba0: 2063 6f70 6965 6420 6173 2d69 732e 2020 copied as-is. \n-00012bb0: 4e6f 726d 616c 6c79 206f 6e65 0a77 6f75 Normally one.wou\n-00012bc0: 6c64 2077 616e 7420 746f 2073 6574 20e2 ld want to set .\n-00012bd0: 8098 6c69 6e65 7769 6474 68e2 8099 2c20 ..linewidth..., \n-00012be0: e280 986c 696e 6573 7479 6c65 e280 992c ...linestyle...,\n-00012bf0: 20e2 8098 6c69 6e65 636f 6c6f 72e2 8099 ...linecolor...\n-00012c00: 2c20 6574 632e 2020 4966 0a6f 6d69 7474 , etc. If.omitt\n-00012c10: 6564 2c20 7468 656e 20e2 8098 6672 616d ed, then ...fram\n-00012c20: 6573 6570 3d30 7074 e280 9920 6973 2061 esep=0pt... is a\n-00012c30: 6464 6564 2073 6f20 7468 6174 2074 6865 dded so that the\n-00012c40: 2066 7261 6d65 2074 6967 6874 6c79 2068 frame tightly h\n-00012c50: 7567 7320 7468 650a e280 9870 7370 6963 ugs the....pspic\n-00012c60: 7475 7265 e280 992e 0a0a 1f0a 4669 6c65 ture........File\n-00012c70: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n-00012c80: 4e6f 6465 3a20 4c61 6e67 7561 6765 2c20 Node: Language, \n-00012c90: 2050 7265 763a 2046 7261 6d65 2c20 2055 Prev: Frame, U\n-00012ca0: 703a 2047 6c6f 6261 6c20 656e 7669 726f p: Global enviro\n-00012cb0: 6e6d 656e 740a 0a33 2e34 2e35 204c 616e nment..3.4.5 Lan\n-00012cc0: 6775 6167 650a 2d2d 2d2d 2d2d 2d2d 2d2d guage.----------\n-00012cd0: 2d2d 2d2d 0a0a 2020 2020 206c 616e 6775 ----.. langu\n-00012ce0: 6167 6520 7469 6b7a 0a20 2020 2020 6c61 age tikz. la\n-00012cf0: 6e67 7561 6765 2074 696b 7a2c 2063 6f6e nguage tikz, con\n-00012d00: 7465 7874 0a20 2020 2020 6c61 6e67 7561 text. langua\n-00012d10: 6765 2070 7374 7269 636b 730a 2020 2020 ge pstricks. \n-00012d20: 206c 616e 6775 6167 6520 7073 7472 6963 language pstric\n-00012d30: 6b73 2c20 6c61 7465 780a 5365 7473 2074 ks, latex.Sets t\n-00012d40: 6865 206f 7574 7075 7420 6c61 6e67 7561 he output langua\n-00012d50: 6765 2067 656e 6572 6174 6564 2062 7920 ge generated by \n-00012d60: e280 9873 6b65 7463 68e2 8099 2e20 2054 ...sketch.... T\n-00012d70: 6865 2073 6574 206f 6620 6f70 7469 6f6e he set of option\n-00012d80: 730a 756e 6465 7273 746f 6f64 2062 7920 s.understood by \n-00012d90: 736b 6574 6368 2061 6c73 6f20 6368 616e sketch also chan\n-00012da0: 6765 732e 2020 466f 7220 6578 616d 706c ges. For exampl\n-00012db0: 652c 2074 6865 20e2 8098 5053 5472 6963 e, the ...PSTric\n-00012dc0: 6b73 e280 9920 6f70 7469 6f6e 0ae2 8098 ks... option....\n-00012dd0: 6c69 6e65 7769 6474 68e2 8099 2077 696c linewidth... wil\n-00012de0: 6c20 6e6f 7420 6265 2070 726f 7065 726c l not be properl\n-00012df0: 7920 6861 6e64 6c65 6420 6966 20e2 8098 y handled if ...\n-00012e00: 6c61 6e67 7561 6765 e280 9920 6973 2073 language... is s\n-00012e10: 6574 2074 6f20 e280 9874 696b 7ae2 8099 et to ...tikz...\n-00012e20: 2e0a 5369 6d69 6c61 726c 792c 2074 6865 ..Similarly, the\n-00012e30: 20e2 8098 5469 6b5a e280 9920 6f70 7469 ...TikZ... opti\n-00012e40: 6f6e 20e2 8098 6c69 6e65 2073 7479 6c65 on ...line style\n-00012e50: e280 9920 286e 6f74 6520 7468 6520 7370 ... (note the sp\n-00012e60: 6163 6529 2077 696c 6c20 6e6f 7420 6265 ace) will not be\n-00012e70: 0a70 726f 7065 726c 7920 6861 6e64 6c65 .properly handle\n-00012e80: 6420 6966 20e2 8098 6c61 6e67 7561 6765 d if ...language\n-00012e90: e280 9920 6973 2073 6574 2074 6f20 e280 ... is set to ..\n-00012ea0: 9870 7374 7269 636b 73e2 8099 2e20 2049 .pstricks.... I\n-00012eb0: 6620 6e6f 206c 616e 6775 6167 6520 6973 f no language is\n-00012ec0: 0a73 7065 6369 6669 6564 2c20 7468 6520 .specified, the \n-00012ed0: 6465 6661 756c 7420 e280 9870 7374 7269 default ...pstri\n-00012ee0: 636b 73e2 8099 2069 7320 7573 6564 2e0a cks... is used..\n-00012ef0: 0a20 2020 416e 206f 7074 696f 6e61 6c20 . An optional \n-00012f00: 636f 6d6d 6120 666f 6c6c 6f77 6564 2062 comma followed b\n-00012f10: 7920 e280 986c 6174 6578 e280 9920 6f72 y ...latex... or\n-00012f20: 20e2 8098 636f 6e74 6578 74e2 8099 2073 ...context... s\n-00012f30: 7065 6369 6669 6573 2074 6865 0a6d 6163 pecifies the.mac\n-00012f40: 726f 2070 6163 6b61 6765 2074 6861 7420 ro package that \n-00012f50: 7468 6520 6f75 7470 7574 2073 686f 756c the output shoul\n-00012f60: 6420 6173 7375 6d65 2e20 2054 6869 7320 d assume. This \n-00012f70: 6166 6665 6374 7320 7468 6520 e280 9870 affects the ...p\n-00012f80: 6963 7475 7265 e280 990a 656e 7669 726f icture....enviro\n-00012f90: 6e6d 656e 7420 636f 6d6d 616e 6473 2065 nment commands e\n-00012fa0: 6d69 7474 6564 2061 6e64 2074 6865 2064 mitted and the d\n-00012fb0: 6f63 756d 656e 7420 7465 6d70 6c61 7465 ocument template\n-00012fc0: 2075 7365 6420 7769 7468 2074 6865 0ae2 used with the..\n-00012fd0: 8098 2d54 e280 9920 6f70 7469 6f6e 2e20 ..-T... option. \n-00012fe0: 202a 4e6f 7465 2043 6f6d 6d61 6e64 206c *Note Command l\n-00012ff0: 696e 653a 3a2e 2020 4e6f 7465 2074 6861 ine::. Note tha\n-00013000: 7420 6174 2074 6865 2074 696d 6520 7468 t at the time th\n-00013010: 6973 206d 616e 7561 6c0a 7761 7320 6765 is manual.was ge\n-00013020: 6e65 7261 7465 642c 20e2 8098 5053 5472 nerated, ...PSTr\n-00013030: 6963 6b73 e280 9920 7761 7320 6e6f 7420 icks... was not \n-00013040: 7375 7070 6f72 7465 6420 6279 204c 6154 supported by LaT\n-00013050: 6558 206f 7220 6279 20e2 8098 436f 6e54 eX or by ...ConT\n-00013060: 6558 74e2 8099 2e0a 0a1f 0a46 696c 653a eXt........File:\n-00013070: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n-00013080: 6f64 653a 2042 7569 6c64 696e 6720 6120 ode: Building a \n-00013090: 6472 6177 696e 672c 2020 4e65 7874 3a20 drawing, Next: \n-000130a0: 436f 6d6d 616e 6420 6c69 6e65 2c20 2050 Command line, P\n-000130b0: 7265 763a 2049 6e70 7574 206c 616e 6775 rev: Input langu\n-000130c0: 6167 652c 2020 5570 3a20 546f 700a 0a34 age, Up: Top..4\n-000130d0: 2042 7569 6c64 696e 6720 6120 6472 6177 Building a draw\n-000130e0: 696e 670a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a ing.************\n-000130f0: 2a2a 2a2a 2a2a 2a2a 0a0a 5375 6363 6573 ********..Succes\n-00013100: 7366 756c 2064 7261 7769 6e67 7320 7769 sful drawings wi\n-00013110: 7468 20e2 8098 736b 6574 6368 e280 9920 th ...sketch... \n-00013120: 616e 6420 7769 7468 2061 6e79 2073 6365 and with any sce\n-00013130: 6e65 2064 6573 6372 6970 7469 6f6e 0a6c ne description.l\n-00013140: 616e 6775 6167 6520 7265 7175 6972 6520 anguage require \n-00013150: 7468 6174 2074 6865 2075 7365 7220 6465 that the user de\n-00013160: 7665 6c6f 7020 616e 2061 6363 7572 6174 velop an accurat\n-00013170: 6520 6d65 6e74 616c 2070 6963 7475 7265 e mental picture\n-00013180: 206f 6620 6865 720a 636f 6465 2061 6e64 of her.code and\n-00013190: 2069 7473 206d 6561 6e69 6e67 2e20 2054 its meaning. T\n-000131a0: 6869 7320 696d 6167 6520 6973 2062 6573 his image is bes\n-000131b0: 7420 6275 696c 7420 696e 2073 6d61 6c6c t built in small\n-000131c0: 2070 6965 6365 732e 0a54 6865 7265 666f pieces..Therefo\n-000131d0: 7265 2c20 e280 9873 6b65 7463 68e2 8099 re, ...sketch...\n-000131e0: 2069 6e70 7574 7320 6172 6520 6265 7374 inputs are best\n-000131f0: 2063 7265 6174 6564 2069 6e20 736d 616c created in smal\n-00013200: 6c20 696e 6372 656d 656e 7473 2077 6974 l increments wit\n-00013210: 680a 6672 6571 7565 6e74 2070 6175 7365 h.frequent pause\n-00013220: 7320 746f 2063 6f6d 7069 6c65 2061 6e64 s to compile and\n-00013230: 2076 6965 7720 7468 6520 7265 7375 6c74 view the result\n-00013240: 732e 2020 4361 7265 6675 6c20 636f 6d6d s. Careful comm\n-00013250: 656e 7473 2069 6e0a 7468 6520 696e 7075 ents in.the inpu\n-00013260: 7420 6f66 7465 6e20 6865 6c70 2061 7320 t often help as \n-00013270: 6120 7363 656e 6520 6772 6f77 7320 696e a scene grows in\n-00013280: 2063 6f6d 706c 6578 6974 792e 0a0a 2a20 complexity...* \n-00013290: 4d65 6e75 3a0a 0a2a 204f 7665 7276 6965 Menu:..* Overvie\n-000132a0: 773a 3a20 2020 2020 2020 2020 2020 2020 w:: \n-000132b0: 2020 2020 2020 2042 7569 6c64 696e 6720 Building \n-000132c0: 6120 7375 6273 7461 6e74 6961 6c20 6472 a substantial dr\n-000132d0: 6177 696e 672e 0a2a 2041 2074 6563 686e awing..* A techn\n-000132e0: 6963 616c 2064 7261 7769 6e67 3a3a 2020 ical drawing:: \n-000132f0: 2020 2020 2020 2041 6e20 6578 616d 706c An exampl\n-00013300: 6520 7769 7468 2066 696e 6520 706c 6163 e with fine plac\n-00013310: 656d 656e 742e 0a2a 2041 2068 6965 7261 ement..* A hiera\n-00013320: 7263 6869 6361 6c20 6d6f 6465 6c3a 3a20 rchical model:: \n-00013330: 2020 2020 2020 2041 6e20 6578 616d 706c An exampl\n-00013340: 6520 7769 7468 2073 7765 6570 7320 616e e with sweeps an\n-00013350: 6420 7075 7473 2e0a 2a20 4361 7665 6174 d puts..* Caveat\n-00013360: 733a 3a20 2020 2020 2020 2020 2020 2020 s:: \n-00013370: 2020 2020 2020 2020 5768 6572 6520 7472 Where tr\n-00013380: 6f75 626c 6520 6361 6e20 6f63 6375 722e ouble can occur.\n-00013390: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-000133a0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 4f76 .info, Node: Ov\n-000133b0: 6572 7669 6577 2c20 204e 6578 743a 2041 erview, Next: A\n-000133c0: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-000133d0: 6e67 2c20 2050 7265 763a 2042 7569 6c64 ng, Prev: Build\n-000133e0: 696e 6720 6120 6472 6177 696e 672c 2020 ing a drawing, \n-000133f0: 5570 3a20 4275 696c 6469 6e67 2061 2064 Up: Building a d\n-00013400: 7261 7769 6e67 0a0a 342e 3120 4f76 6572 rawing..4.1 Over\n-00013410: 7669 6577 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d view.===========\n-00013420: 3d0a 0a41 7320 616e 206f 7665 7276 6965 =..As an overvie\n-00013430: 772c 206c 6574 2773 2064 6576 656c 6f70 w, let's develop\n-00013440: 2061 2064 6961 6772 616d 2074 6861 7420 a diagram that \n-00013450: 7368 6f77 7320 686f 7720 6120 7065 7273 shows how a pers\n-00013460: 7065 6374 6976 650a 7072 6f6a 6563 7469 pective.projecti\n-00013470: 6f6e 2074 7261 6e73 666f 726d 2077 6f72 on transform wor\n-00013480: 6b73 2e20 2057 6527 6c6c 2073 7461 7274 ks. We'll start\n-00013490: 2077 6974 6820 7468 6520 7472 6164 6974 with the tradit\n-000134a0: 696f 6e61 6c20 7265 6665 7265 6e63 650a ional reference.\n-000134b0: 6f62 6a65 6374 2075 7365 6420 696e 2063 object used in c\n-000134c0: 6f6d 7075 7465 7220 6772 6170 6869 6373 omputer graphics\n-000134d0: 2074 6578 7462 6f6f 6b73 2c20 6120 686f textbooks, a ho\n-000134e0: 7573 652d 7368 6170 6564 2070 7269 736d use-shaped prism\n-000134f0: 2e20 2042 6567 696e 0a62 7920 6465 6669 . Begin.by defi\n-00013500: 6e69 6e67 2074 6865 2070 6f69 6e74 7320 ning the points \n-00013510: 6f66 2074 6865 2068 6f75 7365 2e20 2052 of the house. R\n-00013520: 6174 6865 7220 7468 616e 2064 6566 696e ather than defin\n-00013530: 696e 6720 7468 6520 6661 6365 7320 6f66 ing the faces of\n-00013540: 0a74 6865 2068 6f75 7365 2061 7320 706f .the house as po\n-00013550: 6c79 676f 6e73 2061 6e64 2074 7261 6e73 lygons and trans\n-00013560: 666f 726d 696e 6720 7468 6f73 652c 2077 forming those, w\n-00013570: 6520 6172 6520 676f 696e 6720 746f 2074 e are going to t\n-00013580: 7261 6e73 666f 726d 0a74 6865 2070 6f69 ransform.the poi\n-00013590: 6e74 7320 7468 656d 7365 6c76 6573 2077 nts themselves w\n-000135a0: 6974 6820 e280 9873 6b65 7463 68e2 8099 ith ...sketch...\n-000135b0: 2061 7269 7468 6d65 7469 6320 736f 2074 arithmetic so t\n-000135c0: 6861 7420 7765 2068 6176 6520 6e61 6d65 hat we have name\n-000135d0: 7320 666f 720a 7468 6520 7472 616e 7366 s for.the transf\n-000135e0: 6f72 6d65 6420 706f 696e 7473 206c 6174 ormed points lat\n-000135f0: 6572 2e0a 2020 2520 7269 6768 7420 7369 er.. % right si\n-00013600: 6465 2028 6f75 7473 6964 6520 746f 2072 de (outside to r\n-00013610: 6967 6874 290a 2020 6465 6620 5231 2028 ight). def R1 (\n-00013620: 312c 312c 3129 2064 6566 2052 3220 2831 1,1,1) def R2 (1\n-00013630: 2c2d 312c 3129 2064 6566 2052 3320 2831 ,-1,1) def R3 (1\n-00013640: 2c2d 312c 2d31 2920 6465 6620 5234 2028 ,-1,-1) def R4 (\n-00013650: 312c 312c 2d31 290a 2020 6465 6620 5235 1,1,-1). def R5\n-00013660: 2028 312c 312e 352c 3029 0a0a 2020 2520 (1,1.5,0).. % \n-00013670: 6c65 6674 2073 6964 6520 286f 7574 7369 left side (outsi\n-00013680: 6465 2074 6f20 7269 6768 742d 2d62 6163 de to right--bac\n-00013690: 6b77 6172 6429 0a20 2064 6566 2057 2020 kward). def W \n-000136a0: 5b32 2c30 2c30 5d0a 2020 6465 6620 4c31 [2,0,0]. def L1\n-000136b0: 2028 5231 292d 5b57 5d20 6465 6620 4c32 (R1)-[W] def L2\n-000136c0: 2028 5232 292d 5b57 5d20 6465 6620 4c33 (R2)-[W] def L3\n-000136d0: 2028 5233 292d 5b57 5d20 6465 6620 4c34 (R3)-[W] def L4\n-000136e0: 2028 5234 292d 5b57 5d0a 2020 6465 6620 (R4)-[W]. def \n-000136f0: 4c35 2028 5235 292d 5b57 5d0a 546f 2061 L5 (R5)-[W].To a\n-00013700: 6464 2061 2064 6f6f 7220 746f 2074 6865 dd a door to the\n-00013710: 2068 6f75 7365 2c20 7765 2075 7365 2061 house, we use a\n-00013720: 2070 6f6c 7967 6f6e 2073 6c69 6768 746c polygon slightl\n-00013730: 7920 696e 2066 726f 6e74 206f 6620 7468 y in front of th\n-00013740: 650a 666f 7265 6d6f 7374 2066 6163 6520 e.foremost face \n-00013750: 6f66 2074 6865 2068 6f75 7365 2e0a 2020 of the house.. \n-00013760: 2520 646f 6f72 0a20 2064 6566 2065 202e % door. def e .\n-00013770: 3031 0a20 2064 6566 2044 3120 2830 2c2d 01. def D1 (0,-\n-00013780: 312c 312b 6529 2064 6566 2044 3220 282e 1,1+e) def D2 (.\n-00013790: 352c 2d31 2c31 2b65 2920 6465 6620 4433 5,-1,1+e) def D3\n-000137a0: 2028 2e35 2c30 2c31 2b65 2920 6465 6620 (.5,0,1+e) def \n-000137b0: 4434 2028 302c 302c 312b 6529 0a4e 6f77 D4 (0,0,1+e).Now\n-000137c0: 206c 6574 2773 2063 7265 6174 6520 6120 let's create a \n-000137d0: 6e65 7720 7365 7420 6f66 2070 6f69 6e74 new set of point\n-000137e0: 7320 7468 6174 2061 7265 2061 2074 6f2d s that are a to-\n-000137f0: 6265 2d64 6574 6572 6d69 6e65 640a 7472 be-determined.tr\n-00013800: 616e 7366 6f72 6d20 6f66 2074 6865 206f ansform of the o\n-00013810: 7269 6769 6e61 6c73 2e0a 2020 6465 6620 riginals.. def \n-00013820: 6870 2073 6361 6c65 2831 2920 2520 686f hp scale(1) % ho\n-00013830: 7573 6520 706f 7369 7469 6f6e 6572 0a20 use positioner. \n-00013840: 2064 6566 2070 5231 205b 5b68 705d 5d2a def pR1 [[hp]]*\n-00013850: 2852 3129 2064 6566 2070 5232 205b 5b68 (R1) def pR2 [[h\n-00013860: 705d 5d2a 2852 3229 2064 6566 2070 5233 p]]*(R2) def pR3\n-00013870: 205b 5b68 705d 5d2a 2852 3329 0a20 2064 [[hp]]*(R3). d\n-00013880: 6566 2070 5234 205b 5b68 705d 5d2a 2852 ef pR4 [[hp]]*(R\n-00013890: 3429 2064 6566 2070 5235 205b 5b68 705d 4) def pR5 [[hp]\n-000138a0: 5d2a 2852 3529 0a20 2064 6566 2070 4c31 ]*(R5). def pL1\n-000138b0: 205b 5b68 705d 5d2a 284c 3129 2064 6566 [[hp]]*(L1) def\n-000138c0: 2070 4c32 205b 5b68 705d 5d2a 284c 3229 pL2 [[hp]]*(L2)\n-000138d0: 2064 6566 2070 4c33 205b 5b68 705d 5d2a def pL3 [[hp]]*\n-000138e0: 284c 3329 0a20 2064 6566 2070 4c34 205b (L3). def pL4 [\n-000138f0: 5b68 705d 5d2a 284c 3429 2064 6566 2070 [hp]]*(L4) def p\n-00013900: 4c35 205b 5b68 705d 5d2a 284c 3529 0a20 L5 [[hp]]*(L5). \n-00013910: 2064 6566 2070 4431 205b 5b68 705d 5d2a def pD1 [[hp]]*\n-00013920: 2844 3129 2064 6566 2070 4432 205b 5b68 (D1) def pD2 [[h\n-00013930: 705d 5d2a 2844 3229 2064 6566 2070 4433 p]]*(D2) def pD3\n-00013940: 205b 5b68 705d 5d2a 2844 3329 0a20 2064 [[hp]]*(D3). d\n-00013950: 6566 2070 4434 205b 5b68 705d 5d2a 2844 ef pD4 [[hp]]*(D\n-00013960: 3429 200a 4e6f 7465 2074 6865 2075 7365 4) .Note the use\n-00013970: 206f 6620 6120 e280 9c74 7261 6e73 666f of a ...transfo\n-00013980: 726d 2064 6566 696e 6974 696f 6ee2 809d rm definition...\n-00013990: 2061 6e64 20e2 809c 7472 616e 7366 6f72 and ...transfor\n-000139a0: 6d20 7265 6665 7265 6e63 6573 e280 9d2e m references....\n-000139b0: 0a4e 6f77 2064 6566 696e 6520 7468 6520 .Now define the \n-000139c0: 7365 7665 6e20 706f 6c79 676f 6e61 6c20 seven polygonal \n-000139d0: 6661 6365 7320 6f66 2074 6865 2068 6f75 faces of the hou\n-000139e0: 7365 2061 6e64 2074 6865 2064 6f6f 7220 se and the door \n-000139f0: 7573 696e 6720 7468 650a 7472 616e 7366 using the.transf\n-00013a00: 6f72 6d65 6420 706f 696e 7473 2061 7320 ormed points as \n-00013a10: 7665 7274 6963 6573 2e20 2042 6520 6361 vertices. Be ca\n-00013a20: 7265 6675 6c20 7769 7468 2076 6572 7465 reful with verte\n-00013a30: 7820 6f72 6465 7221 0a20 2064 6566 2072 x order!. def r\n-00013a40: 6774 2070 6f6c 7967 6f6e 2028 7052 3129 gt polygon (pR1)\n-00013a50: 2870 5232 2928 7052 3329 2870 5234 2928 (pR2)(pR3)(pR4)(\n-00013a60: 7052 3529 0a20 2064 6566 206c 6674 2070 pR5). def lft p\n-00013a70: 6f6c 7967 6f6e 2028 704c 3529 2870 4c34 olygon (pL5)(pL4\n-00013a80: 2928 704c 3329 2870 4c32 2928 704c 3129 )(pL3)(pL2)(pL1)\n-00013a90: 0a20 2064 6566 2066 7274 2070 6f6c 7967 . def frt polyg\n-00013aa0: 6f6e 2028 7052 3229 2870 5231 2928 704c on (pR2)(pR1)(pL\n-00013ab0: 3129 2870 4c32 290a 2020 6465 6620 6263 1)(pL2). def bc\n-00013ac0: 6b20 706f 6c79 676f 6e20 2870 5234 2928 k polygon (pR4)(\n-00013ad0: 7052 3329 2870 4c33 2928 704c 3429 0a20 pR3)(pL3)(pL4). \n-00013ae0: 2064 6566 2074 6672 2070 6f6c 7967 6f6e def tfr polygon\n-00013af0: 2028 7052 3129 2870 5235 2928 704c 3529 (pR1)(pR5)(pL5)\n-00013b00: 2870 4c31 290a 2020 6465 6620 7462 6b20 (pL1). def tbk \n-00013b10: 706f 6c79 676f 6e20 2870 5235 2928 7052 polygon (pR5)(pR\n-00013b20: 3429 2870 4c34 2928 704c 3529 0a20 2064 4)(pL4)(pL5). d\n-00013b30: 6566 2062 6f74 2070 6f6c 7967 6f6e 2028 ef bot polygon (\n-00013b40: 7052 3229 2870 4c32 2928 704c 3329 2870 pR2)(pL2)(pL3)(p\n-00013b50: 5233 290a 2020 6465 6620 646f 6f72 2070 R3). def door p\n-00013b60: 6f6c 7967 6f6e 5b66 696c 6c63 6f6c 6f72 olygon[fillcolor\n-00013b70: 3d62 726f 776e 5d20 2870 4431 2928 7044 =brown] (pD1)(pD\n-00013b80: 3229 2870 4433 2928 7044 3429 0a20 2064 2)(pD3)(pD4). d\n-00013b90: 6566 2068 6f75 7365 207b 207b 7267 747d ef house { {rgt}\n-00013ba0: 7b6c 6674 7d7b 6672 747d 7b62 636b 7d7b {lft}{frt}{bck}{\n-00013bb0: 7466 727d 7b74 626b 7d7b 626f 747d 7b64 tfr}{tbk}{bot}{d\n-00013bc0: 6f6f 727d 207d 0a20 2020 5469 6d65 2066 oor} }. Time f\n-00013bd0: 6f72 2061 2073 616e 6974 7920 6368 6563 or a sanity chec\n-00013be0: 6b2e 2020 4164 6420 7468 6520 6c69 6e65 k. Add the line\n-00013bf0: 0a20 207b 686f 7573 657d 0a61 6e64 2074 . {house}.and t\n-00013c00: 6869 7320 6973 2077 6861 7420 7765 2067 his is what we g\n-00013c10: 6574 2e0a 0a00 085b 696d 6167 6520 7372 et.....[image sr\n-00013c20: 633d 2265 7831 3330 2e70 6e67 2220 7465 c=\"ex130.png\" te\n-00013c30: 7874 3d22 496d 6167 6520 6578 3133 3020 xt=\"Image ex130 \n-00013c40: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n-00013c50: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n-00013c60: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a54 document.\"..]..T\n-00013c70: 6869 7320 6973 2063 6f72 7265 6374 2c20 his is correct, \n-00013c80: 6275 7420 646f 6573 206e 6f74 2072 6576 but does not rev\n-00013c90: 6561 6c20 7665 7279 206d 7563 682e 2020 eal very much. \n-00013ca0: 436f 6d6d 6f6e 2065 7272 6f72 7320 6172 Common errors ar\n-00013cb0: 650a 6d69 7370 6c61 6365 6420 7665 7274 e.misplaced vert\n-00013cc0: 6963 6573 2061 6e64 2070 6f6c 7967 6f6e ices and polygon\n-00013cd0: 7320 6d69 7373 696e 6720 656e 7469 7265 s missing entire\n-00013ce0: 6c79 2064 7565 2074 6f20 696e 636f 7272 ly due to incorr\n-00013cf0: 6563 7420 7665 7274 6578 0a6f 7264 6572 ect vertex.order\n-00013d00: 2e20 2054 6f20 7275 6c65 2074 6865 7365 . To rule these\n-00013d10: 206f 7574 2c20 6c65 7427 7320 696e 7370 out, let's insp\n-00013d20: 6563 7420 616c 6c20 7369 6465 7320 6f66 ect all sides of\n-00013d30: 2074 6865 2068 6f75 7365 2e20 2054 6869 the house. Thi\n-00013d40: 730a 6973 206e 6f74 2068 6172 642e 2020 s.is not hard. \n-00013d50: 4d65 7265 6c79 2072 6570 6c61 6365 2074 Merely replace t\n-00013d60: 6865 2072 6566 6572 656e 6365 207b 686f he reference {ho\n-00013d70: 7573 657d 2077 6974 6820 6120 e280 9872 use} with a ...r\n-00013d80: 6570 6561 74e2 8099 2e0a 2a4e 6f74 6520 epeat.....*Note \n-00013d90: 5265 7065 6174 733a 3a2e 0a20 2072 6570 Repeats::.. rep\n-00013da0: 6561 7420 7b20 3133 2c20 726f 7461 7465 eat { 13, rotate\n-00013db0: 2833 302c 205b 312c 322c 335d 292c 2074 (30, [1,2,3]), t\n-00013dc0: 7261 6e73 6c61 7465 285b 332c 302c 305d ranslate([3,0,0]\n-00013dd0: 2920 7d20 7b68 6f75 7365 7d0a 0008 5b69 ) } {house}...[i\n-00013de0: 6d61 6765 2073 7263 3d22 6578 3134 302e mage src=\"ex140.\n-00013df0: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n-00013e00: 2065 7831 3430 206f 6d69 7474 6564 2069 ex140 omitted i\n-00013e10: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n-00013e20: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n-00013e30: 2200 085d 0a0a 4167 6169 6e20 7468 696e \"..]..Again thin\n-00013e40: 6773 206c 6f6f 6b20 636f 7272 6563 742e gs look correct.\n-00013e50: 2020 4e6f 7465 2074 6861 7420 7468 6520 Note that the \n-00013e60: 6869 6464 656e 2073 7572 6661 6365 2061 hidden surface a\n-00013e70: 6c67 6f72 6974 686d 0a68 616e 646c 6573 lgorithm.handles\n-00013e80: 2069 6e74 6572 7365 6374 696e 6720 706f intersecting po\n-00013e90: 6c79 676f 6e73 2063 6f72 7265 6374 6c79 lygons correctly\n-00013ea0: 2077 6865 7265 2073 6f6d 6520 636f 7069 where some copi\n-00013eb0: 6573 206f 6620 7468 6520 686f 7573 650a es of the house.\n-00013ec0: 6f76 6572 6c61 702e 0a0a 2020 204c 6574 overlap... Let\n-00013ed0: 2773 206c 6179 206f 7574 2074 6865 2067 's lay out the g\n-00013ee0: 656f 6d65 7472 7920 6f66 2070 6572 7370 eometry of persp\n-00013ef0: 6563 7469 7665 2070 726f 6a65 6374 696f ective projectio\n-00013f00: 6e20 6f66 2074 6865 2068 6f75 7365 0a6f n of the house.o\n-00013f10: 6e74 6f20 6120 706c 616e 6520 7769 7468 nto a plane with\n-00013f20: 2072 6179 7320 7061 7373 696e 6720 7468 rays passing th\n-00013f30: 726f 7567 6820 7468 6520 6f72 6967 696e rough the origin\n-00013f40: 2e20 2042 6567 696e 2062 7920 706f 7369 . Begin by posi\n-00013f50: 7469 6f6e 696e 670a 7468 6520 686f 7573 tioning.the hous\n-00013f60: 6520 7477 656c 7665 2075 6e69 7473 2062 e twelve units b\n-00013f70: 6163 6b20 6f6e 2074 6865 206e 6567 6174 ack on the negat\n-00013f80: 6976 6520 7a2d 6178 6973 2061 6e64 2061 ive z-axis and a\n-00013f90: 6464 696e 6720 6120 7365 7420 6f66 0a63 dding a set of.c\n-00013fa0: 6f6f 7264 696e 6174 6520 6178 6573 2e20 oordinate axes. \n-00013fb0: 2054 6f20 6d6f 7665 2074 6865 2068 6f75 To move the hou\n-00013fc0: 7365 2077 6520 6e65 6564 206f 6e6c 7920 se we need only \n-00013fd0: 6368 616e 6765 2074 6865 2022 686f 7573 change the \"hous\n-00013fe0: 650a 706f 7369 7469 6f6e 696e 6722 2074 e.positioning\" t\n-00013ff0: 7261 6e73 666f 726d 2064 6566 696e 6564 ransform defined\n-00014000: 2065 6172 6c69 6572 2e0a 2020 6465 6620 earlier.. def \n-00014010: 6870 2072 6f74 6174 6528 2d34 302c 205b hp rotate(-40, [\n-00014020: 302c 312c 305d 2920 7468 656e 2074 7261 0,1,0]) then tra\n-00014030: 6e73 6c61 7465 285b 302c 302c 2d31 325d nslate([0,0,-12]\n-00014040: 290a 2020 6465 6620 6178 6573 207b 0a20 ). def axes {. \n-00014050: 2020 2064 6566 2073 7a20 310a 2020 2020 def sz 1. \n-00014060: 6c69 6e65 205b 6172 726f 7773 3d3c 2d3e line [arrows=<->\n-00014070: 5d20 2873 7a2c 302c 3029 284f 2928 302c ] (sz,0,0)(O)(0,\n-00014080: 737a 2c30 290a 2020 2020 6c69 6e65 205b sz,0). line [\n-00014090: 6172 726f 7773 3d2d 3e5d 2020 284f 2928 arrows=->] (O)(\n-000140a0: 302c 302c 737a 290a 2020 2020 6c69 6e65 0,0,sz). line\n-000140b0: 205b 6c69 6e65 7769 6474 683d 2e32 7074 [linewidth=.2pt\n-000140c0: 2c6c 696e 6563 6f6c 6f72 3d62 6c75 652c ,linecolor=blue,\n-000140d0: 6c69 6e65 7374 796c 653d 6461 7368 6564 linestyle=dashed\n-000140e0: 5d20 284f 2928 302c 302c 2d31 3029 0a20 ] (O)(0,0,-10). \n-000140f0: 2020 2073 7065 6369 616c 207c 5c75 7075 special |\\upu\n-00014100: 745b 725d 2331 7b24 7824 7d5c 7570 7574 t[r]#1{$x$}\\uput\n-00014110: 5b75 5d23 327b 2479 247d 5c75 7075 745b [u]#2{$y$}\\uput[\n-00014120: 6c5d 2333 7b24 7a24 7d7c 0a20 2020 2020 l]#3{$z$}|. \n-00014130: 2028 737a 2c30 2c30 2928 302c 737a 2c30 (sz,0,0)(0,sz,0\n-00014140: 2928 302c 302c 737a 290a 2020 7d0a 0a20 )(0,0,sz). }.. \n-00014150: 2020 5469 6d65 2066 6f72 2061 6e6f 7468 Time for anoth\n-00014160: 6572 2074 6573 742e 2020 4c65 7427 7320 er test. Let's \n-00014170: 6275 696c 6420 6120 7265 616c 2076 6965 build a real vie\n-00014180: 7720 7472 616e 7366 6f72 6d2c 2063 7265 w transform, cre\n-00014190: 6174 696e 6720 610a e280 9c76 6972 7475 ating a....virtu\n-000141a0: 616c 2063 616d 6572 61e2 809d 2074 6f20 al camera... to \n-000141b0: 6c6f 6f6b 2061 7420 7468 6520 7363 656e look at the scen\n-000141c0: 6520 7765 2061 7265 2063 6f6e 7374 7275 e we are constru\n-000141d0: 6374 696e 672e 2020 5265 706c 6163 6520 cting. Replace \n-000141e0: 7468 650a e280 9872 6570 6561 74e2 8099 the....repeat...\n-000141f0: 2077 6974 680a 2020 6465 6620 6579 6520 with. def eye \n-00014200: 2831 302c 342c 3130 290a 2020 6465 6620 (10,4,10). def \n-00014210: 6c6f 6f6b 5f61 7420 2830 2c30 2c2d 3529 look_at (0,0,-5)\n-00014220: 0a20 2070 7574 207b 2076 6965 7728 2865 . put { view((e\n-00014230: 7965 292c 2028 6c6f 6f6b 5f61 7429 2920 ye), (look_at)) \n-00014240: 7d20 7b20 7b68 6f75 7365 7d7b 6178 6573 } { {house}{axes\n-00014250: 7d20 7d0a 2020 2054 6865 20e2 809c 7669 } }. The ...vi\n-00014260: 6577 2074 7261 6e73 666f 726d e280 9d20 ew transform... \n-00014270: 7265 706f 7369 7469 6f6e 7320 7468 6520 repositions the \n-00014280: 7363 656e 6520 736f 2074 6861 7420 7468 scene so that th\n-00014290: 6520 706f 696e 7420 e280 9865 7965 e280 e point ...eye..\n-000142a0: 9920 6973 0a61 7420 7468 6520 6f72 6967 . is.at the orig\n-000142b0: 696e 2061 6e64 2074 6865 2064 6972 6563 in and the direc\n-000142c0: 7469 6f6e 2066 726f 6d20 e280 9865 7965 tion from ...eye\n-000142d0: e280 9920 746f 20e2 8098 6c6f 6f6b 5f61 ... to ...look_a\n-000142e0: 74e2 8099 2069 7320 7468 6520 6e65 6761 t... is the nega\n-000142f0: 7469 7665 0a7a 2d61 7869 732e 2020 5468 tive.z-axis. Th\n-00014300: 6973 2072 6571 7569 7265 7320 6120 726f is requires a ro\n-00014310: 7461 7469 6f6e 2061 6e64 2061 2074 7261 tation and a tra\n-00014320: 6e73 6c61 7469 6f6e 2074 6861 7420 6172 nslation that ar\n-00014330: 6520 616c 6c20 7061 636b 6564 0a69 6e74 e all packed.int\n-00014340: 6f20 7468 6520 636f 6e73 7472 7563 746f o the constructo\n-00014350: 7220 e280 9876 6965 77e2 8099 2e0a 0a00 r ...view.......\n-00014360: 085b 696d 6167 6520 7372 633d 2265 7831 .[image src=\"ex1\n-00014370: 3530 2e70 6e67 2220 7465 7874 3d22 496d 50.png\" text=\"Im\n-00014380: 6167 6520 6578 3135 3020 6f6d 6974 7465 age ex150 omitte\n-00014390: 6420 696e 2074 6578 7420 7665 7273 696f d in text versio\n-000143a0: 6e20 6f66 2074 6869 7320 646f 6375 6d65 n of this docume\n-000143b0: 6e74 2e22 0008 5d0a 0a54 6869 7320 6973 nt.\"..]..This is\n-000143c0: 2073 7461 7274 696e 6720 746f 206c 6f6f starting to loo\n-000143d0: 6b20 676f 6f64 2120 2041 6464 2074 6865 k good! Add the\n-000143e0: 2070 726f 6a65 6374 696f 6e20 706c 616e projection plan\n-000143f0: 6520 6861 6c66 2077 6179 0a62 6574 7765 e half way.betwe\n-00014400: 656e 2074 6865 206f 7269 6769 6e20 616e en the origin an\n-00014410: 6420 7468 6520 686f 7573 6520 6174 207a d the house at z\n-00014420: 3d2d 352e 2020 5765 276c 6c20 7472 7920 =-5. We'll try \n-00014430: 7468 6520 616e 676c 6520 6172 6775 6d65 the angle argume\n-00014440: 6e74 0a66 6561 7475 7265 206f 6620 e280 nt.feature of ..\n-00014450: 9873 7065 6369 616c e280 9920 746f 2070 .special... to p\n-00014460: 6f73 6974 696f 6e20 6120 6c61 6265 6c2e osition a label.\n-00014470: 0a20 2064 6566 2070 2035 2025 2070 726f . def p 5 % pro\n-00014480: 6a65 6374 696f 6e20 6469 7374 616e 6365 jection distance\n-00014490: 2028 706c 616e 6520 6174 207a 3d2d 7029 (plane at z=-p)\n-000144a0: 0a20 2064 6566 2070 726f 6a65 6374 696f . def projectio\n-000144b0: 6e5f 706c 616e 6520 7b0a 2020 2020 6465 n_plane {. de\n-000144c0: 6620 737a 2031 2e35 0a20 2020 2070 6f6c f sz 1.5. pol\n-000144d0: 7967 6f6e 2028 2d73 7a2c 2d73 7a2c 2d70 ygon (-sz,-sz,-p\n-000144e0: 2928 737a 2c2d 737a 2c2d 7029 2873 7a2c )(sz,-sz,-p)(sz,\n-000144f0: 737a 2c2d 7029 282d 737a 2c73 7a2c 2d70 sz,-p)(-sz,sz,-p\n-00014500: 290a 2020 2020 7370 6563 6961 6c20 7c5c ). special |\\\n-00014510: 7270 7574 5b62 5d23 312d 3223 337b 5c66 rput[b]#1-2#3{\\f\n-00014520: 6f6f 746e 6f74 6573 697a 655c 7366 2070 ootnotesize\\sf p\n-00014530: 726f 6a65 6374 696f 6e20 706c 616e 657d rojection plane}\n-00014540: 7c20 0a20 2020 2020 2028 2d73 7a2c 2d73 | . (-sz,-s\n-00014550: 7a2c 2d70 2928 737a 2c2d 737a 2c2d 7029 z,-p)(sz,-sz,-p)\n-00014560: 2830 2c2d 737a 2b2e 312c 2d70 290a 2020 (0,-sz+.1,-p). \n-00014570: 7d0a 4164 6420 7b70 726f 6a65 6374 696f }.Add {projectio\n-00014580: 6e5f 706c 616e 657d 2074 6f20 7468 6520 n_plane} to the \n-00014590: 6c69 7374 206f 6620 6f62 6a65 6374 7320 list of objects \n-000145a0: 696e 2074 6865 20e2 8098 7075 74e2 8099 in the ...put...\n-000145b0: 2061 626f 7665 2e0a 0a00 085b 696d 6167 above.....[imag\n-000145c0: 6520 7372 633d 2265 7831 3630 2e70 6e67 e src=\"ex160.png\n-000145d0: 2220 7465 7874 3d22 496d 6167 6520 6578 \" text=\"Image ex\n-000145e0: 3136 3020 6f6d 6974 7465 6420 696e 2074 160 omitted in t\n-000145f0: 6578 7420 7665 7273 696f 6e20 6f66 2074 ext version of t\n-00014600: 6869 7320 646f 6375 6d65 6e74 2e22 0008 his document.\"..\n-00014610: 5d0a 0a20 2020 5468 6520 7761 7920 7765 ].. The way we\n-00014620: 2063 6f6e 7374 7275 6374 6564 2074 6865 constructed the\n-00014630: 2070 6f69 6e74 7320 6f66 2074 6865 2068 points of the h\n-00014640: 6f75 7365 206e 6f77 206d 616b 6573 2069 ouse now makes i\n-00014650: 7420 6561 7379 2074 6f0a 6472 6177 2072 t easy to.draw r\n-00014660: 6179 7320 6f66 2070 726f 6a65 6374 696f ays of projectio\n-00014670: 6e2e 2020 5765 276c 6c20 6361 7374 206f n. We'll cast o\n-00014680: 6e65 2072 6179 2066 726f 6d20 6576 6572 ne ray from ever\n-00014690: 7920 7669 7369 626c 6520 7665 7274 6578 y visible vertex\n-000146a0: 0a6f 6620 7468 6520 686f 7573 6520 616e .of the house an\n-000146b0: 6420 6465 6669 6e65 206f 7074 696f 6e73 d define options\n-000146c0: 2073 6f20 7468 6520 6170 7065 6172 616e so the appearan\n-000146d0: 6365 206f 6620 616c 6c20 7261 7973 2063 ce of all rays c\n-000146e0: 616e 2062 650a 6368 616e 6765 6420 6174 an be.changed at\n-000146f0: 2074 6865 2073 616d 6520 7469 6d65 2e0a the same time..\n-00014700: 2020 6465 6620 7072 6f6a 6563 7469 6f6e def projection\n-00014710: 5f72 6179 7320 7b0a 2020 2020 6465 6620 _rays {. def \n-00014720: 7261 796f 7074 205b 6c69 6e65 7769 6474 rayopt [linewidt\n-00014730: 683d 2e33 7074 2c6c 696e 6563 6f6c 6f72 h=.3pt,linecolor\n-00014740: 3d6c 6967 6874 6772 6179 5d0a 2020 2020 =lightgray]. \n-00014750: 6c69 6e65 205b 7261 796f 7074 5d28 4f29 line [rayopt](O)\n-00014760: 2870 5231 2920 6c69 6e65 205b 7261 796f (pR1) line [rayo\n-00014770: 7074 5d28 4f29 2870 5232 2920 6c69 6e65 pt](O)(pR2) line\n-00014780: 5b72 6179 6f70 745d 284f 2928 7052 3329 [rayopt](O)(pR3)\n-00014790: 0a20 2020 206c 696e 6520 5b72 6179 6f70 . line [rayop\n-000147a0: 745d 284f 2928 7052 3429 206c 696e 6520 t](O)(pR4) line \n-000147b0: 5b72 6179 6f70 745d 284f 2928 7052 3529 [rayopt](O)(pR5)\n-000147c0: 0a20 2020 206c 696e 6520 5b72 6179 6f70 . line [rayop\n-000147d0: 745d 284f 2928 704c 3129 206c 696e 6520 t](O)(pL1) line \n-000147e0: 5b72 6179 6f70 745d 284f 2928 704c 3229 [rayopt](O)(pL2)\n-000147f0: 206c 696e 655b 7261 796f 7074 5d28 4f29 line[rayopt](O)\n-00014800: 2870 4c35 290a 2020 2020 6c69 6e65 205b (pL5). line [\n-00014810: 7261 796f 7074 5d28 4f29 2870 4431 2920 rayopt](O)(pD1) \n-00014820: 6c69 6e65 205b 7261 796f 7074 5d28 4f29 line [rayopt](O)\n-00014830: 2870 4432 2920 0a20 2020 206c 696e 6520 (pD2) . line \n-00014840: 5b72 6179 6f70 745d 284f 2928 7044 3329 [rayopt](O)(pD3)\n-00014850: 206c 696e 6520 5b72 6179 6f70 745d 284f line [rayopt](O\n-00014860: 2928 7044 3429 200a 2020 7d0a 5468 6520 )(pD4) . }.The \n-00014870: 7265 7375 6c74 2069 7320 7368 6f77 6e20 result is shown \n-00014880: 6865 7265 2e0a 0a00 085b 696d 6167 6520 here.....[image \n-00014890: 7372 633d 2265 7831 3730 2e70 6e67 2220 src=\"ex170.png\" \n-000148a0: 7465 7874 3d22 496d 6167 6520 6578 3137 text=\"Image ex17\n-000148b0: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n-000148c0: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n-000148d0: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n-000148e0: 0a54 6865 2072 6179 7320 7069 6572 6365 .The rays pierce\n-000148f0: 2074 6865 2070 726f 6a65 6374 696f 6e20 the projection \n-00014900: 706c 616e 6520 6174 2074 6865 2063 6f72 plane at the cor\n-00014910: 7265 7370 6f6e 6469 6e67 2070 6f69 6e74 responding point\n-00014920: 7320 6f6e 2074 6865 0a70 6572 7370 6563 s on the.perspec\n-00014930: 7469 7665 2069 6d61 6765 2077 6520 6172 tive image we ar\n-00014940: 6520 7472 7969 6e67 2074 6f20 6472 6177 e trying to draw\n-00014950: 2e20 2041 6c62 7265 6368 7420 44c3 bc72 . Albrecht D..r\n-00014960: 6572 2061 6e64 2068 6973 0a52 656e 6169 er and his.Renai\n-00014970: 7373 616e 6365 2063 6f6e 7465 6d70 6f72 ssance contempor\n-00014980: 6172 6965 7320 6861 6420 7468 6520 7361 aries had the sa\n-00014990: 6d65 2069 6465 6120 696e 2074 6865 2065 me idea in the e\n-000149a0: 6172 6c79 2031 3530 3027 732e 0a0a 0008 arly 1500's.....\n-000149b0: 5b69 6d61 6765 2073 7263 3d22 6475 6572 [image src=\"duer\n-000149c0: 6572 2e70 6e67 2220 7465 7874 3d22 496d er.png\" text=\"Im\n-000149d0: 6167 6520 6f66 2044 7565 7265 7227 7320 age of Duerer's \n-000149e0: 7065 7273 7065 6374 6976 6520 636f 6d70 perspective comp\n-000149f0: 7574 6572 206f 6d69 7474 6564 2069 6e20 uter omitted in \n-00014a00: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n-00014a10: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n-00014a20: 085d 0a0a 2020 2041 6c6c 2074 6861 7427 .].. All that'\n-00014a30: 7320 6c65 6674 2069 7320 746f 2066 696e s left is to fin\n-00014a40: 6420 6120 7761 7920 746f 2063 6f6e 6e65 d a way to conne\n-00014a50: 6374 2074 6865 2070 6f69 6e74 7320 6f66 ct the points of\n-00014a60: 2074 6865 2068 6f75 7365 0a6f 6e20 7468 the house.on th\n-00014a70: 6520 7072 6f6a 6563 7469 6f6e 2070 6c61 e projection pla\n-00014a80: 6e65 2e20 2057 6520 636f 756c 6420 7075 ne. We could pu\n-00014a90: 6c6c 206f 7574 2061 2067 6f6f 6420 636f ll out a good co\n-00014aa0: 6d70 7574 6572 2067 7261 7068 6963 730a mputer graphics.\n-00014ab0: 7465 7874 2c20 6669 6e64 2074 6865 206e text, find the n\n-00014ac0: 6563 6573 7361 7279 206d 6174 7269 782c ecessary matrix,\n-00014ad0: 2061 6e64 2065 6e74 6572 2069 7420 6f75 and enter it ou\n-00014ae0: 7273 656c 7665 7320 6173 2061 2074 7261 rselves as a tra\n-00014af0: 6e73 666f 726d 0a6c 6974 6572 616c 2e20 nsform.literal. \n-00014b00: 202a 4e6f 7465 2054 7261 6e73 666f 726d *Note Transform\n-00014b10: 206c 6974 6572 616c 733a 3a2e 2020 5468 literals::. Th\n-00014b20: 6174 2077 6f72 6b20 6973 2061 6c72 6561 at work is alrea\n-00014b30: 6479 2064 6f6e 652c 0a68 6f77 6576 6572 dy done,.however\n-00014b40: 2e20 2057 6520 6361 6e20 7573 6520 7468 . We can use th\n-00014b50: 6520 e280 9870 726f 6a65 6374 2870 29e2 e ...project(p).\n-00014b60: 8099 2063 6f6e 7374 7275 6374 6f72 2e0a .. constructor..\n-00014b70: 0a20 2020 5468 6572 6520 6172 6520 7374 . There are st\n-00014b80: 696c 6c20 736f 6d65 2064 6574 6169 6c73 ill some details\n-00014b90: 2074 6861 7420 7265 7175 6972 6520 6361 that require ca\n-00014ba0: 7265 2e20 2050 726f 6a65 6374 696f 6e20 re. Projection \n-00014bb0: 7769 6c6c 0a66 6c61 7474 656e 2077 6861 will.flatten wha\n-00014bc0: 7465 7665 7220 6973 2074 7261 6e73 666f tever is transfo\n-00014bd0: 726d 6564 206f 6e74 6f20 7468 6520 706c rmed onto the pl\n-00014be0: 616e 6520 7a3d 2d70 2e20 2054 6865 7265 ane z=-p. There\n-00014bf0: 666f 7265 2061 6e79 2070 6172 740a 6f66 fore any part.of\n-00014c00: 2074 6865 2068 6f75 7365 2063 6f75 6c64 the house could\n-00014c10: 2064 6973 6170 7065 6172 2062 6568 696e disappear behin\n-00014c20: 6420 7468 6520 7072 6f6a 6563 7469 6f6e d the projection\n-00014c30: 2070 6c61 6e65 2028 7468 6520 6869 6464 plane (the hidd\n-00014c40: 656e 0a73 7572 6661 6365 2061 6c67 6f72 en.surface algor\n-00014c50: 6974 686d 206f 7264 6572 7320 6f62 6a65 ithm orders obje\n-00014c60: 6374 7320 6174 2074 6865 2073 616d 6520 cts at the same \n-00014c70: 6465 7074 6820 6172 6269 7472 6172 696c depth arbitraril\n-00014c80: 7929 2e20 2054 6865 0a64 6f6f 7220 6d61 y). The.door ma\n-00014c90: 7920 616c 736f 2064 6973 6170 7065 6172 y also disappear\n-00014ca0: 2062 6568 696e 6420 7468 6520 6672 6f6e behind the fron\n-00014cb0: 7420 6f66 2074 6865 2068 6f75 7365 2e20 t of the house. \n-00014cc0: 2054 6f20 6d61 6b65 2073 7572 650a 6576 To make sure.ev\n-00014cd0: 6572 7974 6869 6e67 2072 656d 6169 6e73 erything remains\n-00014ce0: 2076 6973 6962 6c65 2c20 7765 276c 6c20 visible, we'll \n-00014cf0: 706c 6163 6520 7468 6520 686f 7573 6520 place the house \n-00014d00: 6120 7469 6e79 2062 6974 2069 6e20 6672 a tiny bit in fr\n-00014d10: 6f6e 7420 6f66 0a74 6865 2070 726f 6a65 ont of.the proje\n-00014d20: 6374 696f 6e20 706c 616e 6520 616e 6420 ction plane and \n-00014d30: 6120 7365 636f 6e64 2063 6f70 7920 6f66 a second copy of\n-00014d40: 2074 6865 2064 6f6f 7220 696e 2066 726f the door in fro\n-00014d50: 6e74 206f 6620 7468 650a 686f 7573 652e nt of the.house.\n-00014d60: 0a20 2064 6566 2070 726f 6a65 6374 696f . def projectio\n-00014d70: 6e20 7b0a 2020 2020 2520 6520 6973 2061 n {. % e is a\n-00014d80: 2073 6d61 6c6c 206e 756d 6265 7220 6465 small number de\n-00014d90: 6669 6e65 6420 6162 6f76 650a 2020 2020 fined above. \n-00014da0: 7075 7420 7b20 7072 6f6a 6563 7428 7029 put { project(p)\n-00014db0: 2074 6865 6e20 7472 616e 736c 6174 6528 then translate(\n-00014dc0: 5b30 2c30 2c31 2a65 5d29 207d 207b 686f [0,0,1*e]) } {ho\n-00014dd0: 7573 657d 0a20 2020 2070 7574 207b 2070 use}. put { p\n-00014de0: 726f 6a65 6374 2870 2920 7468 656e 2074 roject(p) then t\n-00014df0: 7261 6e73 6c61 7465 285b 302c 302c 322a ranslate([0,0,2*\n-00014e00: 655d 2920 7d20 7b64 6f6f 727d 0a20 207d e]) } {door}. }\n-00014e10: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22 ....[image src=\"\n-00014e20: 6578 3138 302e 706e 6722 2074 6578 743d ex180.png\" text=\n-00014e30: 2249 6d61 6765 2065 7831 3830 206f 6d69 \"Image ex180 omi\n-00014e40: 7474 6564 2069 6e20 7465 7874 2076 6572 tted in text ver\n-00014e50: 7369 6f6e 206f 6620 7468 6973 2064 6f63 sion of this doc\n-00014e60: 756d 656e 742e 2200 085d 0a0a 2020 2049 ument.\"..].. I\n-00014e70: 6620 796f 7520 6861 7665 2073 7475 6469 f you have studi\n-00014e80: 6564 2061 6e64 2075 6e64 6572 7374 616e ed and understan\n-00014e90: 6420 616c 6c20 7468 6973 2c20 796f 7520 d all this, you \n-00014ea0: 6172 6520 7765 6c6c 206f 6e20 7468 6520 are well on the \n-00014eb0: 7761 790a 746f 2073 7563 6365 7373 2077 way.to success w\n-00014ec0: 6974 6820 e280 9873 6b65 7463 68e2 8099 ith ...sketch...\n-00014ed0: 2e20 204e 6f74 2073 686f 776e 2061 7265 . Not shown are\n-00014ee0: 2074 6865 2032 3020 6f72 2073 6f20 6974 the 20 or so it\n-00014ef0: 6572 6174 696f 6e73 2074 6861 740a 7765 erations that.we\n-00014f00: 7265 2072 6571 7569 7265 6420 746f 2066 re required to f\n-00014f10: 696e 6420 6120 7265 6173 6f6e 6162 6c65 ind a reasonable\n-00014f20: 2076 6965 7769 6e67 2061 6e67 6c65 2061 viewing angle a\n-00014f30: 6e64 2068 6f75 7365 2070 6f73 6974 696f nd house positio\n-00014f40: 6e2c 0a65 7463 2e20 204e 6f6e 6574 6865 n,.etc. Nonethe\n-00014f50: 6c65 7373 2c20 7468 6973 2064 7261 7769 less, this drawi\n-00014f60: 6e67 2077 6173 2063 6f6d 706c 6574 6564 ng was completed\n-00014f70: 2069 6e20 6162 6f75 7420 616e 2068 6f75 in about an hou\n-00014f80: 722e 2020 5768 696c 6520 610a 4755 4920 r. While a.GUI \n-00014f90: 746f 6f6c 206d 6179 2068 6176 6520 6265 tool may have be\n-00014fa0: 656e 2061 206c 6974 746c 6520 6661 7374 en a little fast\n-00014fb0: 6572 2c20 6974 2069 7320 756e 6c69 6b65 er, it is unlike\n-00014fc0: 6c79 2074 6861 7420 6120 6e65 770a 6472 ly that a new.dr\n-00014fd0: 6177 696e 672c 2069 7473 656c 6620 6120 awing, itself a \n-00014fe0: 7065 7273 7065 6374 6976 6520 7072 6f6a perspective proj\n-00014ff0: 6563 7469 6f6e 206f 6620 7468 6520 7363 ection of the sc\n-00015000: 656e 652c 2063 6f75 6c64 2062 650a 6765 ene, could be.ge\n-00015010: 6e65 7261 7465 6420 7769 7468 2074 776f nerated with two\n-00015020: 206d 6f72 6520 6d69 6e75 7465 7327 2077 more minutes' w\n-00015030: 6f72 6b21 2020 4a75 7374 2063 6861 6e67 ork! Just chang\n-00015040: 6520 7468 6520 7669 6577 2074 7261 6e73 e the view trans\n-00015050: 666f 726d 0a74 6f0a 2020 7075 7420 7b20 form.to. put { \n-00015060: 7669 6577 2828 6579 6529 2c20 286c 6f6f view((eye), (loo\n-00015070: 6b5f 6174 2929 2074 6865 6e20 7065 7273 k_at)) then pers\n-00015080: 7065 6374 6976 6528 3929 207d 207b 202e pective(9) } { .\n-00015090: 2e2e 0a61 6e64 2070 726f 6475 6365 2074 ...and produce t\n-000150a0: 6869 732e 0a0a 0008 5b69 6d61 6765 2073 his.....[image s\n-000150b0: 7263 3d22 6578 3139 302e 706e 6722 2074 rc=\"ex190.png\" t\n-000150c0: 6578 743d 2249 6d61 6765 2065 7831 3930 ext=\"Image ex190\n-000150d0: 206f 6d69 7474 6564 2069 6e20 7465 7874 omitted in text\n-000150e0: 2076 6572 7369 6f6e 206f 6620 7468 6973 version of this\n-000150f0: 2064 6f63 756d 656e 742e 2200 085d 0a0a document.\"..]..\n-00015100: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n-00015110: 6e66 6f2c 2020 4e6f 6465 3a20 4120 7465 nfo, Node: A te\n-00015120: 6368 6e69 6361 6c20 6472 6177 696e 672c chnical drawing,\n-00015130: 2020 4e65 7874 3a20 4120 6869 6572 6172 Next: A hierar\n-00015140: 6368 6963 616c 206d 6f64 656c 2c20 2050 chical model, P\n-00015150: 7265 763a 204f 7665 7276 6965 772c 2020 rev: Overview, \n-00015160: 5570 3a20 4275 696c 6469 6e67 2061 2064 Up: Building a d\n-00015170: 7261 7769 6e67 0a0a 342e 3220 4120 7465 rawing..4.2 A te\n-00015180: 6368 6e69 6361 6c20 6472 6177 696e 670a chnical drawing.\n+00011d30: 2d2d 2d2d 2d2d 2d2d 2d2d 0a73 6361 6c61 ----------.scala\n+00011d40: 7220 2020 2020 20e2 8098 4944 e280 990a r ...ID....\n+00011d50: 706f 696e 7420 2020 2020 2020 e280 9828 point ...(\n+00011d60: 4944 29e2 8099 0a76 6563 746f 7220 2020 ID)....vector \n+00011d70: 2020 20e2 8098 5b49 445d e280 990a 7472 ...[ID]....tr\n+00011d80: 616e 7366 6f72 6d20 2020 e280 985b 5b49 ansform ...[[I\n+00011d90: 445d 5de2 8099 0a64 7261 7761 626c 6520 D]]....drawable \n+00011da0: 2020 20e2 8098 7b49 447d e280 990a 6f70 ...{ID}....op\n+00011db0: 7469 6f6e 7320 2020 2020 e280 985b 4944 tions ...[ID\n+00011dc0: 5de2 8099 206f 7220 e280 985b 4944 312c ]... or ...[ID1,\n+00011dd0: 2e2e 2e2c 4944 4e5d e280 990a 7461 6720 ...,IDN]....tag \n+00011de0: 2020 2020 2020 2020 e280 983c 4944 3ee2 ....\n+00011df0: 8099 0a0a 4e6f 7465 2074 6861 7420 7371 ....Note that sq\n+00011e00: 7561 7265 2062 7261 636b 6574 7320 e280 uare brackets ..\n+00011e10: 985b 205d e280 9920 6172 6520 7573 6564 .[ ]... are used\n+00011e20: 2062 6f74 6820 666f 7220 7665 6374 6f72 both for vector\n+00011e30: 2061 6e64 2066 6f72 206f 7074 696f 6e73 and for options\n+00011e40: 0a72 6566 6572 656e 6365 732e 2020 4465 .references. De\n+00011e50: 7461 696c 7320 6f66 20e2 8098 736b 6574 tails of ...sket\n+00011e60: 6368 e280 9920 7379 6e74 6178 206d 616b ch... syntax mak\n+00011e70: 6520 6974 2069 6d70 6f73 7369 626c 6520 e it impossible \n+00011e80: 666f 7220 7468 6573 6520 7477 6f0a 7265 for these two.re\n+00011e90: 6665 7265 6e63 6520 7479 7065 7320 746f ference types to\n+00011ea0: 2062 6520 636f 6e66 7573 6564 2e20 2054 be confused. T\n+00011eb0: 6865 2073 7065 6369 616c 206d 756c 7469 he special multi\n+00011ec0: 706c 6520 7265 6665 7265 6e63 650a e280 ple reference...\n+00011ed0: 985b 4944 312c 4944 322c 2e2e 2e2c 4944 .[ID1,ID2,...,ID\n+00011ee0: 4e5d e280 9920 6163 7473 2061 7320 6966 N]... acts as if\n+00011ef0: 2074 6865 2072 6573 7065 6374 6976 6520 the respective \n+00011f00: 6c69 7374 7320 6f66 206f 7074 696f 6e73 lists of options\n+00011f10: 2077 6572 650a 636f 6e63 6174 656e 6174 were.concatenat\n+00011f20: 6564 2e0a 0a1f 0a46 696c 653a 2073 6b65 ed.....File: ske\n+00011f30: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n+00011f40: 2047 6c6f 6261 6c20 656e 7669 726f 6e6d Global environm\n+00011f50: 656e 742c 2020 5072 6576 3a20 4465 6669 ent, Prev: Defi\n+00011f60: 6e69 7469 6f6e 732c 2020 5570 3a20 496e nitions, Up: In\n+00011f70: 7075 7420 6c61 6e67 7561 6765 0a0a 332e put language..3.\n+00011f80: 3420 476c 6f62 616c 2065 6e76 6972 6f6e 4 Global environ\n+00011f90: 6d65 6e74 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d ment.===========\n+00011fa0: 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a 0a41 6e20 ===========..An \n+00011fb0: 6f70 7469 6f6e 616c 2067 6c6f 6261 6c20 optional global \n+00011fc0: 656e 7669 726f 6e6d 656e 7420 626c 6f63 environment bloc\n+00011fd0: 6b20 7072 6f76 6964 6573 2061 2066 6577 k provides a few\n+00011fe0: 2077 6179 7320 746f 2061 6666 6563 7420 ways to affect \n+00011ff0: 7468 650a 656e 7469 7265 2073 6365 6e65 the.entire scene\n+00012000: 2e20 2054 6865 2062 6c6f 636b 206d 7573 . The block mus\n+00012010: 7420 6170 7065 6172 2061 7320 7468 6520 t appear as the \n+00012020: 6c61 7374 2074 6578 7420 696e 2074 6865 last text in the\n+00012030: 20e2 8098 736b 6574 6368 e280 990a 696e ...sketch....in\n+00012040: 7075 7420 6669 6c65 2e20 2049 7420 6d61 put file. It ma\n+00012050: 7920 696e 636c 7564 6520 6465 6669 6e69 y include defini\n+00012060: 7469 6f6e 732c 2062 7574 206e 6f74 6520 tions, but note \n+00012070: 7468 6174 2070 7265 7669 6f75 730a 6465 that previous.de\n+00012080: 6669 6e69 7469 6f6e 7320 6174 2074 6865 finitions at the\n+00012090: 2074 6f70 206c 6576 656c 2028 6e6f 7420 top level (not \n+000120a0: 6e65 7374 6564 2069 6e73 6964 6520 626c nested inside bl\n+000120b0: 6f63 6b73 2920 6172 6520 616c 736f 0a61 ocks) are also.a\n+000120c0: 7661 696c 6162 6c65 2e0a 0a2a 5379 6e74 vailable...*Synt\n+000120d0: 6178 3a2a 0a20 2020 2020 676c 6f62 616c ax:*. global\n+000120e0: 207b 2045 4e56 4952 4f4e 4d45 4e54 5f53 { ENVIRONMENT_S\n+000120f0: 4554 5449 4e47 5320 7d0a 5468 6520 636f ETTINGS }.The co\n+00012100: 6e74 656e 7473 206f 6620 454e 5649 524f ntents of ENVIRO\n+00012110: 4e4d 454e 545f 5345 5454 494e 4753 2061 NMENT_SETTINGS a\n+00012120: 7265 2064 6973 6375 7373 6564 2069 6e20 re discussed in \n+00012130: 7468 6520 7365 6374 696f 6e73 2074 6861 the sections tha\n+00012140: 740a 666f 6c6c 6f77 2e0a 0a2a 204d 656e t.follow...* Men\n+00012150: 753a 0a0a 2a20 476c 6f62 616c 206f 7074 u:..* Global opt\n+00012160: 696f 6e73 3a3a 2020 2020 2020 2020 2020 ions:: \n+00012170: 2020 2020 4174 7472 6962 7574 6573 206f Attributes o\n+00012180: 6620 7468 6520 656e 7469 7265 2064 7261 f the entire dra\n+00012190: 7769 6e67 2e0a 2a20 4361 6d65 7261 3a3a wing..* Camera::\n+000121a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000121b0: 2020 2020 2020 4120 6669 6e61 6c20 6361 A final ca\n+000121c0: 6d65 7261 2074 7261 6e73 666f 726d 6174 mera transformat\n+000121d0: 696f 6e20 6f66 2074 6865 2073 6365 6e65 ion of the scene\n+000121e0: 2e0a 2a20 5069 6374 7572 6520 626f 783a ..* Picture box:\n+000121f0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00012200: 2020 5365 7474 696e 6720 7468 6520 626f Setting the bo\n+00012210: 756e 6469 6e67 2062 6f78 2061 6e64 2032 unding box and 2\n+00012220: 6420 636c 6970 7069 6e67 2e0a 2a20 4672 d clipping..* Fr\n+00012230: 616d 653a 3a20 2020 2020 2020 2020 2020 ame:: \n+00012240: 2020 2020 2020 2020 2020 2020 4164 6469 Addi\n+00012250: 6e67 2061 2062 6f78 2061 726f 756e 6420 ng a box around \n+00012260: 7468 6520 6472 6177 696e 672e 0a2a 204c the drawing..* L\n+00012270: 616e 6775 6167 653a 3a20 2020 2020 2020 anguage:: \n+00012280: 2020 2020 2020 2020 2020 2020 2053 6574 Set\n+00012290: 7469 6e67 2074 6865 206f 7574 7075 7420 ting the output \n+000122a0: 6c61 6e67 7561 6765 2e0a 0a1f 0a46 696c language.....Fil\n+000122b0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n+000122c0: 204e 6f64 653a 2047 6c6f 6261 6c20 6f70 Node: Global op\n+000122d0: 7469 6f6e 732c 2020 4e65 7874 3a20 4361 tions, Next: Ca\n+000122e0: 6d65 7261 2c20 2050 7265 763a 2047 6c6f mera, Prev: Glo\n+000122f0: 6261 6c20 656e 7669 726f 6e6d 656e 742c bal environment,\n+00012300: 2020 5570 3a20 476c 6f62 616c 2065 6e76 Up: Global env\n+00012310: 6972 6f6e 6d65 6e74 0a0a 332e 342e 3120 ironment..3.4.1 \n+00012320: 476c 6f62 616c 206f 7074 696f 6e73 0a2d Global options.-\n+00012330: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n+00012340: 2d2d 2d0a 0a2a 5379 6e74 6178 3a2a 0a20 ---..*Syntax:*. \n+00012350: 2020 2020 7365 7420 5b20 4f50 5449 4f4e set [ OPTION\n+00012360: 5320 5d0a 5468 6520 636f 6e74 656e 7473 S ].The contents\n+00012370: 206f 6620 4f50 5449 4f4e 532c 2065 7863 of OPTIONS, exc\n+00012380: 6570 7420 666f 7220 e280 9873 6b65 7463 ept for ...sketc\n+00012390: 68e2 8099 2069 6e74 6572 6e61 6c20 6f70 h... internal op\n+000123a0: 7469 6f6e 732c 2061 7265 0a63 6f70 6965 tions, are.copie\n+000123b0: 6420 6173 2d69 7320 746f 2061 205c 7073 d as-is to a \\ps\n+000123c0: 7365 7420 7468 6174 2061 7070 6561 7273 set that appears\n+000123d0: 2062 6566 6f72 6520 616e 7974 6869 6e67 before anything\n+000123e0: 2065 6c73 6520 696e 2074 6865 206f 7574 else in the out\n+000123f0: 7075 740a 6669 6c65 2e20 2054 6869 7320 put.file. This \n+00012400: 6973 2061 2067 6f6f 6420 706c 6163 6520 is a good place \n+00012410: 746f 2073 6574 20e2 8098 756e 6974 e280 to set ...unit..\n+00012420: 992c 2061 2064 6566 6175 6c74 20e2 8098 ., a default ...\n+00012430: 6c69 6e65 7769 6474 68e2 8099 2c20 6574 linewidth..., et\n+00012440: 632e 0a0a 2020 2049 6e74 6572 6e61 6c20 c... Internal \n+00012450: 6f70 7469 6f6e 7320 776f 726b 206f 6e20 options work on \n+00012460: 616c 6c20 6f62 6a65 6374 7320 7768 6572 all objects wher\n+00012470: 6520 7468 6579 206d 616b 6520 7365 6e73 e they make sens\n+00012480: 652e 2020 5468 6973 0a69 6e63 6c75 6465 e. This.include\n+00012490: 7320 e280 9863 756c 6ce2 8099 2061 6e64 s ...cull... and\n+000124a0: 20e2 8098 7370 6c69 74e2 8099 2028 6275 ...split... (bu\n+000124b0: 7420 6e6f 7420 e280 986c 6179 e280 9929 t not ...lay...)\n+000124c0: 2e20 202a 4e6f 7465 2049 6e74 6572 6e61 . *Note Interna\n+000124d0: 6c20 6f70 7469 6f6e 733a 3a2e 0a0a 1f0a l options::.....\n+000124e0: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+000124f0: 6f2c 2020 4e6f 6465 3a20 4361 6d65 7261 o, Node: Camera\n+00012500: 2c20 204e 6578 743a 2050 6963 7475 7265 , Next: Picture\n+00012510: 2062 6f78 2c20 2050 7265 763a 2047 6c6f box, Prev: Glo\n+00012520: 6261 6c20 6f70 7469 6f6e 732c 2020 5570 bal options, Up\n+00012530: 3a20 476c 6f62 616c 2065 6e76 6972 6f6e : Global environ\n+00012540: 6d65 6e74 0a0a 332e 342e 3220 4361 6d65 ment..3.4.2 Came\n+00012550: 7261 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a ra.------------.\n+00012560: 0a2a 5379 6e74 6178 3a2a 0a20 2020 2020 .*Syntax:*. \n+00012570: 6361 6d65 7261 2054 5241 4e53 464f 524d camera TRANSFORM\n+00012580: 5f45 5850 5245 5353 494f 4e0a 2020 2054 _EXPRESSION. T\n+00012590: 6865 2054 5241 4e53 464f 524d 5f45 5850 he TRANSFORM_EXP\n+000125a0: 5245 5353 494f 4e20 6973 2061 7070 6c69 RESSION is appli\n+000125b0: 6564 2061 6674 6572 2061 6c6c 206f 7468 ed after all oth\n+000125c0: 6572 2074 7261 6e73 666f 726d 6174 696f er transformatio\n+000125d0: 6e73 0a6f 6620 7468 6520 7363 656e 652e ns.of the scene.\n+000125e0: 2020 5468 6973 2069 7320 6375 7272 656e This is curren\n+000125f0: 746c 7920 6f6e 6c79 2075 7365 6675 6c20 tly only useful \n+00012600: 666f 7220 7472 616e 7366 6f72 6d69 6e67 for transforming\n+00012610: 2074 6865 0a62 6f75 6e64 696e 6720 626f the.bounding bo\n+00012620: 782e 2020 2a4e 6f74 6520 5069 6374 7572 x. *Note Pictur\n+00012630: 6520 626f 783a 3a2e 2020 4974 2077 696c e box::. It wil\n+00012640: 6c20 706c 6179 2061 2072 6f6c 6520 696e l play a role in\n+00012650: 2061 6e79 2066 7574 7572 650a 696d 706c any future.impl\n+00012660: 656d 656e 7461 7469 6f6e 206f 6620 636c ementation of cl\n+00012670: 6970 7069 6e67 2e0a 0a1f 0a46 696c 653a ipping.....File:\n+00012680: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+00012690: 6f64 653a 2050 6963 7475 7265 2062 6f78 ode: Picture box\n+000126a0: 2c20 204e 6578 743a 2046 7261 6d65 2c20 , Next: Frame, \n+000126b0: 2050 7265 763a 2043 616d 6572 612c 2020 Prev: Camera, \n+000126c0: 5570 3a20 476c 6f62 616c 2065 6e76 6972 Up: Global envir\n+000126d0: 6f6e 6d65 6e74 0a0a 332e 342e 3320 5069 onment..3.4.3 Pi\n+000126e0: 6374 7572 6520 626f 780a 2d2d 2d2d 2d2d cture box.------\n+000126f0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d0a 0a2a 5379 -----------..*Sy\n+00012700: 6e74 6178 3a2a 0a20 2020 2020 7069 6374 ntax:*. pict\n+00012710: 7572 6562 6f78 5b42 4153 454c 494e 455d urebox[BASELINE]\n+00012720: 0a20 2020 2020 7069 6374 7572 6562 6f78 . picturebox\n+00012730: 5b42 4153 454c 494e 455d 2028 5031 2928 [BASELINE] (P1)(\n+00012740: 5032 290a 5468 6520 6669 7273 7420 666f P2).The first fo\n+00012750: 726d 206f 6620 e280 9870 6963 7475 7265 rm of ...picture\n+00012760: 626f 78e2 8099 2063 6175 7365 7320 6120 box... causes a \n+00012770: 7363 616c 6172 2042 4153 454c 494e 4520 scalar BASELINE \n+00012780: 6672 6163 7469 6f6e 2074 6f20 6265 0a65 fraction to be.e\n+00012790: 6d69 7474 6564 2069 6e20 7468 6520 e280 mitted in the ..\n+000127a0: 9870 7370 6963 7475 7265 e280 9920 656e .pspicture... en\n+000127b0: 7669 726f 6e6d 656e 7420 6f66 2074 6865 vironment of the\n+000127c0: 206f 7574 7075 742e 2020 5365 6520 e280 output. See ..\n+000127d0: 9850 5354 7269 636b 73e2 8099 0a64 6f63 .PSTricks....doc\n+000127e0: 756d 656e 7461 7469 6f6e 2066 6f72 20e2 umentation for .\n+000127f0: 8098 7073 7069 6374 7572 65e2 8099 2e0a ..pspicture.....\n+00012800: 0a20 2020 496e 2074 6865 2073 6563 6f6e . In the secon\n+00012810: 6420 666f 726d 2c20 7468 6520 4241 5345 d form, the BASE\n+00012820: 4c49 4e45 2066 7261 6374 696f 6e20 6973 LINE fraction is\n+00012830: 206f 7074 696f 6e61 6c2c 2061 6e64 2074 optional, and t\n+00012840: 6865 2074 776f 0a70 6f69 6e74 7320 7468 he two.points th\n+00012850: 6174 2066 6f6c 6c6f 7720 6465 6669 6e65 at follow define\n+00012860: 2074 6865 2064 6961 676f 6e61 6c20 6f66 the diagonal of\n+00012870: 2061 2074 6872 6565 2d64 696d 656e 7369 a three-dimensi\n+00012880: 6f6e 616c 2062 6f75 6e64 696e 670a 626f onal bounding.bo\n+00012890: 7820 666f 7220 7468 6520 636f 6d70 6c65 x for the comple\n+000128a0: 7465 6420 7363 656e 652e 2020 5468 6520 ted scene. The \n+000128b0: 7061 7261 6c6c 656c 2070 726f 6a65 6374 parallel project\n+000128c0: 696f 6e20 6f66 2074 6865 2062 6f75 6e64 ion of the bound\n+000128d0: 696e 670a 626f 7820 6465 7465 726d 696e ing.box determin\n+000128e0: 6573 2074 6865 2063 6f72 6e65 7273 206f es the corners o\n+000128f0: 6620 7468 6520 6472 6177 696e 6727 7320 f the drawing's \n+00012900: e280 9870 7370 6963 7475 7265 2ae2 8099 ...pspicture*...\n+00012910: 2065 6e76 6972 6f6e 6d65 6e74 2c0a 7768 environment,.wh\n+00012920: 6963 6820 6973 2075 7365 6420 696e 2070 ich is used in p\n+00012930: 6c61 6365 206f 6620 e280 9870 7370 6963 lace of ...pspic\n+00012940: 7475 7265 e280 992e 2020 5468 6973 2063 ture.... This c\n+00012950: 6175 7365 7320 506f 7374 5363 7269 7074 auses PostScript\n+00012960: 2074 6f20 636c 6970 0a74 6865 2066 696e to clip.the fin\n+00012970: 616c 2064 7261 7769 6e67 2074 6f20 7468 al drawing to th\n+00012980: 6520 626f 756e 6469 6e67 2062 6f78 2069 e bounding box i\n+00012990: 6e20 3264 2e20 2049 6620 7468 6572 6520 n 2d. If there \n+000129a0: 6973 2061 20e2 8098 6361 6d65 7261 e280 is a ...camera..\n+000129b0: 990a 7370 6563 6966 6965 642c 2074 6865 ..specified, the\n+000129c0: 2063 616d 6572 6120 7472 616e 666f 726d camera tranform\n+000129d0: 6174 696f 6e20 6973 2061 7070 6c69 6564 ation is applied\n+000129e0: 2074 6f20 7468 6520 626f 756e 6469 6e67 to the bounding\n+000129f0: 2062 6f78 2c20 616e 640a 7468 6520 e280 box, and.the ..\n+00012a00: 9870 7370 6963 7475 7265 e280 9920 6973 .pspicture... is\n+00012a10: 2073 6574 206a 7573 7420 6c61 7267 6520 set just large \n+00012a20: 656e 6f75 6768 2074 6f20 696e 636c 7564 enough to includ\n+00012a30: 6520 7468 6520 7472 616e 7366 6f72 6d65 e the transforme\n+00012a40: 6420 626f 782e 0a0a 2020 2057 6865 6e20 d box... When \n+00012a50: 6e6f 2062 6f75 6e64 696e 6720 626f 7820 no bounding box \n+00012a60: 6973 2067 6976 656e 2c20 e280 9873 6b65 is given, ...ske\n+00012a70: 7463 68e2 8099 2063 6f6d 7075 7465 7320 tch... computes \n+00012a80: 6f6e 6520 6175 746f 6d61 7469 6361 6c6c one automaticall\n+00012a90: 792e 0a0a 1f0a 4669 6c65 3a20 736b 6574 y.....File: sket\n+00012aa0: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+00012ab0: 4672 616d 652c 2020 4e65 7874 3a20 4c61 Frame, Next: La\n+00012ac0: 6e67 7561 6765 2c20 2050 7265 763a 2050 nguage, Prev: P\n+00012ad0: 6963 7475 7265 2062 6f78 2c20 2055 703a icture box, Up:\n+00012ae0: 2047 6c6f 6261 6c20 656e 7669 726f 6e6d Global environm\n+00012af0: 656e 740a 0a33 2e34 2e34 2046 7261 6d65 ent..3.4.4 Frame\n+00012b00: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 2a53 .-----------..*S\n+00012b10: 796e 7461 783a 2a0a 2020 2020 2066 7261 yntax:*. fra\n+00012b20: 6d65 205b 4f50 5449 4f4e 535d 0a43 6175 me [OPTIONS].Cau\n+00012b30: 7365 7320 6120 5c70 7366 7261 6d65 626f ses a \\psframebo\n+00012b40: 7820 746f 2073 7572 726f 756e 6420 7468 x to surround th\n+00012b50: 6520 e280 9870 7370 6963 7475 7265 e280 e ...pspicture..\n+00012b60: 9920 656e 7669 726f 6e6d 656e 7420 696e . environment in\n+00012b70: 2074 6865 0a6f 7574 7075 742e 2020 4966 the.output. If\n+00012b80: 204f 5054 494f 4e53 2061 7265 2070 7265 OPTIONS are pre\n+00012b90: 7365 6e74 2c20 7468 6579 2061 7265 2063 sent, they are c\n+00012ba0: 6f70 6965 6420 6173 2d69 732e 2020 4e6f opied as-is. No\n+00012bb0: 726d 616c 6c79 206f 6e65 0a77 6f75 6c64 rmally one.would\n+00012bc0: 2077 616e 7420 746f 2073 6574 20e2 8098 want to set ...\n+00012bd0: 6c69 6e65 7769 6474 68e2 8099 2c20 e280 linewidth..., ..\n+00012be0: 986c 696e 6573 7479 6c65 e280 992c 20e2 .linestyle..., .\n+00012bf0: 8098 6c69 6e65 636f 6c6f 72e2 8099 2c20 ..linecolor..., \n+00012c00: 6574 632e 2020 4966 0a6f 6d69 7474 6564 etc. If.omitted\n+00012c10: 2c20 7468 656e 20e2 8098 6672 616d 6573 , then ...frames\n+00012c20: 6570 3d30 7074 e280 9920 6973 2061 6464 ep=0pt... is add\n+00012c30: 6564 2073 6f20 7468 6174 2074 6865 2066 ed so that the f\n+00012c40: 7261 6d65 2074 6967 6874 6c79 2068 7567 rame tightly hug\n+00012c50: 7320 7468 650a e280 9870 7370 6963 7475 s the....pspictu\n+00012c60: 7265 e280 992e 0a0a 1f0a 4669 6c65 3a20 re........File: \n+00012c70: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+00012c80: 6465 3a20 4c61 6e67 7561 6765 2c20 2050 de: Language, P\n+00012c90: 7265 763a 2046 7261 6d65 2c20 2055 703a rev: Frame, Up:\n+00012ca0: 2047 6c6f 6261 6c20 656e 7669 726f 6e6d Global environm\n+00012cb0: 656e 740a 0a33 2e34 2e35 204c 616e 6775 ent..3.4.5 Langu\n+00012cc0: 6167 650a 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d age.------------\n+00012cd0: 2d2d 0a0a 2020 2020 206c 616e 6775 6167 --.. languag\n+00012ce0: 6520 7469 6b7a 0a20 2020 2020 6c61 6e67 e tikz. lang\n+00012cf0: 7561 6765 2074 696b 7a2c 2063 6f6e 7465 uage tikz, conte\n+00012d00: 7874 0a20 2020 2020 6c61 6e67 7561 6765 xt. language\n+00012d10: 2070 7374 7269 636b 730a 2020 2020 206c pstricks. l\n+00012d20: 616e 6775 6167 6520 7073 7472 6963 6b73 anguage pstricks\n+00012d30: 2c20 6c61 7465 780a 5365 7473 2074 6865 , latex.Sets the\n+00012d40: 206f 7574 7075 7420 6c61 6e67 7561 6765 output language\n+00012d50: 2067 656e 6572 6174 6564 2062 7920 e280 generated by ..\n+00012d60: 9873 6b65 7463 68e2 8099 2e20 2054 6865 .sketch.... The\n+00012d70: 2073 6574 206f 6620 6f70 7469 6f6e 730a set of options.\n+00012d80: 756e 6465 7273 746f 6f64 2062 7920 736b understood by sk\n+00012d90: 6574 6368 2061 6c73 6f20 6368 616e 6765 etch also change\n+00012da0: 732e 2020 466f 7220 6578 616d 706c 652c s. For example,\n+00012db0: 2074 6865 20e2 8098 5053 5472 6963 6b73 the ...PSTricks\n+00012dc0: e280 9920 6f70 7469 6f6e 0ae2 8098 6c69 ... option....li\n+00012dd0: 6e65 7769 6474 68e2 8099 2077 696c 6c20 newidth... will \n+00012de0: 6e6f 7420 6265 2070 726f 7065 726c 7920 not be properly \n+00012df0: 6861 6e64 6c65 6420 6966 20e2 8098 6c61 handled if ...la\n+00012e00: 6e67 7561 6765 e280 9920 6973 2073 6574 nguage... is set\n+00012e10: 2074 6f20 e280 9874 696b 7ae2 8099 2e0a to ...tikz.....\n+00012e20: 5369 6d69 6c61 726c 792c 2074 6865 20e2 Similarly, the .\n+00012e30: 8098 5469 6b5a e280 9920 6f70 7469 6f6e ..TikZ... option\n+00012e40: 20e2 8098 6c69 6e65 2073 7479 6c65 e280 ...line style..\n+00012e50: 9920 286e 6f74 6520 7468 6520 7370 6163 . (note the spac\n+00012e60: 6529 2077 696c 6c20 6e6f 7420 6265 0a70 e) will not be.p\n+00012e70: 726f 7065 726c 7920 6861 6e64 6c65 6420 roperly handled \n+00012e80: 6966 20e2 8098 6c61 6e67 7561 6765 e280 if ...language..\n+00012e90: 9920 6973 2073 6574 2074 6f20 e280 9870 . is set to ...p\n+00012ea0: 7374 7269 636b 73e2 8099 2e20 2049 6620 stricks.... If \n+00012eb0: 6e6f 206c 616e 6775 6167 6520 6973 0a73 no language is.s\n+00012ec0: 7065 6369 6669 6564 2c20 7468 6520 6465 pecified, the de\n+00012ed0: 6661 756c 7420 e280 9870 7374 7269 636b fault ...pstrick\n+00012ee0: 73e2 8099 2069 7320 7573 6564 2e0a 0a20 s... is used... \n+00012ef0: 2020 416e 206f 7074 696f 6e61 6c20 636f An optional co\n+00012f00: 6d6d 6120 666f 6c6c 6f77 6564 2062 7920 mma followed by \n+00012f10: e280 986c 6174 6578 e280 9920 6f72 20e2 ...latex... or .\n+00012f20: 8098 636f 6e74 6578 74e2 8099 2073 7065 ..context... spe\n+00012f30: 6369 6669 6573 2074 6865 0a6d 6163 726f cifies the.macro\n+00012f40: 2070 6163 6b61 6765 2074 6861 7420 7468 package that th\n+00012f50: 6520 6f75 7470 7574 2073 686f 756c 6420 e output should \n+00012f60: 6173 7375 6d65 2e20 2054 6869 7320 6166 assume. This af\n+00012f70: 6665 6374 7320 7468 6520 e280 9870 6963 fects the ...pic\n+00012f80: 7475 7265 e280 990a 656e 7669 726f 6e6d ture....environm\n+00012f90: 656e 7420 636f 6d6d 616e 6473 2065 6d69 ent commands emi\n+00012fa0: 7474 6564 2061 6e64 2074 6865 2064 6f63 tted and the doc\n+00012fb0: 756d 656e 7420 7465 6d70 6c61 7465 2075 ument template u\n+00012fc0: 7365 6420 7769 7468 2074 6865 0ae2 8098 sed with the....\n+00012fd0: 2d54 e280 9920 6f70 7469 6f6e 2e20 202a -T... option. *\n+00012fe0: 4e6f 7465 2043 6f6d 6d61 6e64 206c 696e Note Command lin\n+00012ff0: 653a 3a2e 2020 4e6f 7465 2074 6861 7420 e::. Note that \n+00013000: 6174 2074 6865 2074 696d 6520 7468 6973 at the time this\n+00013010: 206d 616e 7561 6c0a 7761 7320 6765 6e65 manual.was gene\n+00013020: 7261 7465 642c 20e2 8098 5053 5472 6963 rated, ...PSTric\n+00013030: 6b73 e280 9920 7761 7320 6e6f 7420 7375 ks... was not su\n+00013040: 7070 6f72 7465 6420 6279 204c 6154 6558 pported by LaTeX\n+00013050: 206f 7220 6279 20e2 8098 436f 6e54 6558 or by ...ConTeX\n+00013060: 74e2 8099 2e0a 0a1f 0a46 696c 653a 2073 t........File: s\n+00013070: 6b65 7463 682e 696e 666f 2c20 204e 6f64 ketch.info, Nod\n+00013080: 653a 2042 7569 6c64 696e 6720 6120 6472 e: Building a dr\n+00013090: 6177 696e 672c 2020 4e65 7874 3a20 436f awing, Next: Co\n+000130a0: 6d6d 616e 6420 6c69 6e65 2c20 2050 7265 mmand line, Pre\n+000130b0: 763a 2049 6e70 7574 206c 616e 6775 6167 v: Input languag\n+000130c0: 652c 2020 5570 3a20 546f 700a 0a34 2042 e, Up: Top..4 B\n+000130d0: 7569 6c64 696e 6720 6120 6472 6177 696e uilding a drawin\n+000130e0: 670a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a 2a2a g.**************\n+000130f0: 2a2a 2a2a 2a2a 0a0a 5375 6363 6573 7366 ******..Successf\n+00013100: 756c 2064 7261 7769 6e67 7320 7769 7468 ul drawings with\n+00013110: 20e2 8098 736b 6574 6368 e280 9920 616e ...sketch... an\n+00013120: 6420 7769 7468 2061 6e79 2073 6365 6e65 d with any scene\n+00013130: 2064 6573 6372 6970 7469 6f6e 0a6c 616e description.lan\n+00013140: 6775 6167 6520 7265 7175 6972 6520 7468 guage require th\n+00013150: 6174 2074 6865 2075 7365 7220 6465 7665 at the user deve\n+00013160: 6c6f 7020 616e 2061 6363 7572 6174 6520 lop an accurate \n+00013170: 6d65 6e74 616c 2070 6963 7475 7265 206f mental picture o\n+00013180: 6620 6865 720a 636f 6465 2061 6e64 2069 f her.code and i\n+00013190: 7473 206d 6561 6e69 6e67 2e20 2054 6869 ts meaning. Thi\n+000131a0: 7320 696d 6167 6520 6973 2062 6573 7420 s image is best \n+000131b0: 6275 696c 7420 696e 2073 6d61 6c6c 2070 built in small p\n+000131c0: 6965 6365 732e 0a54 6865 7265 666f 7265 ieces..Therefore\n+000131d0: 2c20 e280 9873 6b65 7463 68e2 8099 2069 , ...sketch... i\n+000131e0: 6e70 7574 7320 6172 6520 6265 7374 2063 nputs are best c\n+000131f0: 7265 6174 6564 2069 6e20 736d 616c 6c20 reated in small \n+00013200: 696e 6372 656d 656e 7473 2077 6974 680a increments with.\n+00013210: 6672 6571 7565 6e74 2070 6175 7365 7320 frequent pauses \n+00013220: 746f 2063 6f6d 7069 6c65 2061 6e64 2076 to compile and v\n+00013230: 6965 7720 7468 6520 7265 7375 6c74 732e iew the results.\n+00013240: 2020 4361 7265 6675 6c20 636f 6d6d 656e Careful commen\n+00013250: 7473 2069 6e0a 7468 6520 696e 7075 7420 ts in.the input \n+00013260: 6f66 7465 6e20 6865 6c70 2061 7320 6120 often help as a \n+00013270: 7363 656e 6520 6772 6f77 7320 696e 2063 scene grows in c\n+00013280: 6f6d 706c 6578 6974 792e 0a0a 2a20 4d65 omplexity...* Me\n+00013290: 6e75 3a0a 0a2a 204f 7665 7276 6965 773a nu:..* Overview:\n+000132a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+000132b0: 2020 2020 2042 7569 6c64 696e 6720 6120 Building a \n+000132c0: 7375 6273 7461 6e74 6961 6c20 6472 6177 substantial draw\n+000132d0: 696e 672e 0a2a 2041 2074 6563 686e 6963 ing..* A technic\n+000132e0: 616c 2064 7261 7769 6e67 3a3a 2020 2020 al drawing:: \n+000132f0: 2020 2020 2041 6e20 6578 616d 706c 6520 An example \n+00013300: 7769 7468 2066 696e 6520 706c 6163 656d with fine placem\n+00013310: 656e 742e 0a2a 2041 2068 6965 7261 7263 ent..* A hierarc\n+00013320: 6869 6361 6c20 6d6f 6465 6c3a 3a20 2020 hical model:: \n+00013330: 2020 2020 2041 6e20 6578 616d 706c 6520 An example \n+00013340: 7769 7468 2073 7765 6570 7320 616e 6420 with sweeps and \n+00013350: 7075 7473 2e0a 2a20 4361 7665 6174 733a puts..* Caveats:\n+00013360: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00013370: 2020 2020 2020 5768 6572 6520 7472 6f75 Where trou\n+00013380: 626c 6520 6361 6e20 6f63 6375 722e 0a0a ble can occur...\n+00013390: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+000133a0: 6e66 6f2c 2020 4e6f 6465 3a20 4f76 6572 nfo, Node: Over\n+000133b0: 7669 6577 2c20 204e 6578 743a 2041 2074 view, Next: A t\n+000133c0: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+000133d0: 2c20 2050 7265 763a 2042 7569 6c64 696e , Prev: Buildin\n+000133e0: 6720 6120 6472 6177 696e 672c 2020 5570 g a drawing, Up\n+000133f0: 3a20 4275 696c 6469 6e67 2061 2064 7261 : Building a dra\n+00013400: 7769 6e67 0a0a 342e 3120 4f76 6572 7669 wing..4.1 Overvi\n+00013410: 6577 0a3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d0a ew.============.\n+00013420: 0a41 7320 616e 206f 7665 7276 6965 772c .As an overview,\n+00013430: 206c 6574 2773 2064 6576 656c 6f70 2061 let's develop a\n+00013440: 2064 6961 6772 616d 2074 6861 7420 7368 diagram that sh\n+00013450: 6f77 7320 686f 7720 6120 7065 7273 7065 ows how a perspe\n+00013460: 6374 6976 650a 7072 6f6a 6563 7469 6f6e ctive.projection\n+00013470: 2074 7261 6e73 666f 726d 2077 6f72 6b73 transform works\n+00013480: 2e20 2057 6527 6c6c 2073 7461 7274 2077 . We'll start w\n+00013490: 6974 6820 7468 6520 7472 6164 6974 696f ith the traditio\n+000134a0: 6e61 6c20 7265 6665 7265 6e63 650a 6f62 nal reference.ob\n+000134b0: 6a65 6374 2075 7365 6420 696e 2063 6f6d ject used in com\n+000134c0: 7075 7465 7220 6772 6170 6869 6373 2074 puter graphics t\n+000134d0: 6578 7462 6f6f 6b73 2c20 6120 686f 7573 extbooks, a hous\n+000134e0: 652d 7368 6170 6564 2070 7269 736d 2e20 e-shaped prism. \n+000134f0: 2042 6567 696e 0a62 7920 6465 6669 6e69 Begin.by defini\n+00013500: 6e67 2074 6865 2070 6f69 6e74 7320 6f66 ng the points of\n+00013510: 2074 6865 2068 6f75 7365 2e20 2052 6174 the house. Rat\n+00013520: 6865 7220 7468 616e 2064 6566 696e 696e her than definin\n+00013530: 6720 7468 6520 6661 6365 7320 6f66 0a74 g the faces of.t\n+00013540: 6865 2068 6f75 7365 2061 7320 706f 6c79 he house as poly\n+00013550: 676f 6e73 2061 6e64 2074 7261 6e73 666f gons and transfo\n+00013560: 726d 696e 6720 7468 6f73 652c 2077 6520 rming those, we \n+00013570: 6172 6520 676f 696e 6720 746f 2074 7261 are going to tra\n+00013580: 6e73 666f 726d 0a74 6865 2070 6f69 6e74 nsform.the point\n+00013590: 7320 7468 656d 7365 6c76 6573 2077 6974 s themselves wit\n+000135a0: 6820 e280 9873 6b65 7463 68e2 8099 2061 h ...sketch... a\n+000135b0: 7269 7468 6d65 7469 6320 736f 2074 6861 rithmetic so tha\n+000135c0: 7420 7765 2068 6176 6520 6e61 6d65 7320 t we have names \n+000135d0: 666f 720a 7468 6520 7472 616e 7366 6f72 for.the transfor\n+000135e0: 6d65 6420 706f 696e 7473 206c 6174 6572 med points later\n+000135f0: 2e0a 2020 2520 7269 6768 7420 7369 6465 .. % right side\n+00013600: 2028 6f75 7473 6964 6520 746f 2072 6967 (outside to rig\n+00013610: 6874 290a 2020 6465 6620 5231 2028 312c ht). def R1 (1,\n+00013620: 312c 3129 2064 6566 2052 3220 2831 2c2d 1,1) def R2 (1,-\n+00013630: 312c 3129 2064 6566 2052 3320 2831 2c2d 1,1) def R3 (1,-\n+00013640: 312c 2d31 2920 6465 6620 5234 2028 312c 1,-1) def R4 (1,\n+00013650: 312c 2d31 290a 2020 6465 6620 5235 2028 1,-1). def R5 (\n+00013660: 312c 312e 352c 3029 0a0a 2020 2520 6c65 1,1.5,0).. % le\n+00013670: 6674 2073 6964 6520 286f 7574 7369 6465 ft side (outside\n+00013680: 2074 6f20 7269 6768 742d 2d62 6163 6b77 to right--backw\n+00013690: 6172 6429 0a20 2064 6566 2057 2020 5b32 ard). def W [2\n+000136a0: 2c30 2c30 5d0a 2020 6465 6620 4c31 2028 ,0,0]. def L1 (\n+000136b0: 5231 292d 5b57 5d20 6465 6620 4c32 2028 R1)-[W] def L2 (\n+000136c0: 5232 292d 5b57 5d20 6465 6620 4c33 2028 R2)-[W] def L3 (\n+000136d0: 5233 292d 5b57 5d20 6465 6620 4c34 2028 R3)-[W] def L4 (\n+000136e0: 5234 292d 5b57 5d0a 2020 6465 6620 4c35 R4)-[W]. def L5\n+000136f0: 2028 5235 292d 5b57 5d0a 546f 2061 6464 (R5)-[W].To add\n+00013700: 2061 2064 6f6f 7220 746f 2074 6865 2068 a door to the h\n+00013710: 6f75 7365 2c20 7765 2075 7365 2061 2070 ouse, we use a p\n+00013720: 6f6c 7967 6f6e 2073 6c69 6768 746c 7920 olygon slightly \n+00013730: 696e 2066 726f 6e74 206f 6620 7468 650a in front of the.\n+00013740: 666f 7265 6d6f 7374 2066 6163 6520 6f66 foremost face of\n+00013750: 2074 6865 2068 6f75 7365 2e0a 2020 2520 the house.. % \n+00013760: 646f 6f72 0a20 2064 6566 2065 202e 3031 door. def e .01\n+00013770: 0a20 2064 6566 2044 3120 2830 2c2d 312c . def D1 (0,-1,\n+00013780: 312b 6529 2064 6566 2044 3220 282e 352c 1+e) def D2 (.5,\n+00013790: 2d31 2c31 2b65 2920 6465 6620 4433 2028 -1,1+e) def D3 (\n+000137a0: 2e35 2c30 2c31 2b65 2920 6465 6620 4434 .5,0,1+e) def D4\n+000137b0: 2028 302c 302c 312b 6529 0a4e 6f77 206c (0,0,1+e).Now l\n+000137c0: 6574 2773 2063 7265 6174 6520 6120 6e65 et's create a ne\n+000137d0: 7720 7365 7420 6f66 2070 6f69 6e74 7320 w set of points \n+000137e0: 7468 6174 2061 7265 2061 2074 6f2d 6265 that are a to-be\n+000137f0: 2d64 6574 6572 6d69 6e65 640a 7472 616e -determined.tran\n+00013800: 7366 6f72 6d20 6f66 2074 6865 206f 7269 sform of the ori\n+00013810: 6769 6e61 6c73 2e0a 2020 6465 6620 6870 ginals.. def hp\n+00013820: 2073 6361 6c65 2831 2920 2520 686f 7573 scale(1) % hous\n+00013830: 6520 706f 7369 7469 6f6e 6572 0a20 2064 e positioner. d\n+00013840: 6566 2070 5231 205b 5b68 705d 5d2a 2852 ef pR1 [[hp]]*(R\n+00013850: 3129 2064 6566 2070 5232 205b 5b68 705d 1) def pR2 [[hp]\n+00013860: 5d2a 2852 3229 2064 6566 2070 5233 205b ]*(R2) def pR3 [\n+00013870: 5b68 705d 5d2a 2852 3329 0a20 2064 6566 [hp]]*(R3). def\n+00013880: 2070 5234 205b 5b68 705d 5d2a 2852 3429 pR4 [[hp]]*(R4)\n+00013890: 2064 6566 2070 5235 205b 5b68 705d 5d2a def pR5 [[hp]]*\n+000138a0: 2852 3529 0a20 2064 6566 2070 4c31 205b (R5). def pL1 [\n+000138b0: 5b68 705d 5d2a 284c 3129 2064 6566 2070 [hp]]*(L1) def p\n+000138c0: 4c32 205b 5b68 705d 5d2a 284c 3229 2064 L2 [[hp]]*(L2) d\n+000138d0: 6566 2070 4c33 205b 5b68 705d 5d2a 284c ef pL3 [[hp]]*(L\n+000138e0: 3329 0a20 2064 6566 2070 4c34 205b 5b68 3). def pL4 [[h\n+000138f0: 705d 5d2a 284c 3429 2064 6566 2070 4c35 p]]*(L4) def pL5\n+00013900: 205b 5b68 705d 5d2a 284c 3529 0a20 2064 [[hp]]*(L5). d\n+00013910: 6566 2070 4431 205b 5b68 705d 5d2a 2844 ef pD1 [[hp]]*(D\n+00013920: 3129 2064 6566 2070 4432 205b 5b68 705d 1) def pD2 [[hp]\n+00013930: 5d2a 2844 3229 2064 6566 2070 4433 205b ]*(D2) def pD3 [\n+00013940: 5b68 705d 5d2a 2844 3329 0a20 2064 6566 [hp]]*(D3). def\n+00013950: 2070 4434 205b 5b68 705d 5d2a 2844 3429 pD4 [[hp]]*(D4)\n+00013960: 200a 4e6f 7465 2074 6865 2075 7365 206f .Note the use o\n+00013970: 6620 6120 e280 9c74 7261 6e73 666f 726d f a ...transform\n+00013980: 2064 6566 696e 6974 696f 6ee2 809d 2061 definition... a\n+00013990: 6e64 20e2 809c 7472 616e 7366 6f72 6d20 nd ...transform \n+000139a0: 7265 6665 7265 6e63 6573 e280 9d2e 0a4e references.....N\n+000139b0: 6f77 2064 6566 696e 6520 7468 6520 7365 ow define the se\n+000139c0: 7665 6e20 706f 6c79 676f 6e61 6c20 6661 ven polygonal fa\n+000139d0: 6365 7320 6f66 2074 6865 2068 6f75 7365 ces of the house\n+000139e0: 2061 6e64 2074 6865 2064 6f6f 7220 7573 and the door us\n+000139f0: 696e 6720 7468 650a 7472 616e 7366 6f72 ing the.transfor\n+00013a00: 6d65 6420 706f 696e 7473 2061 7320 7665 med points as ve\n+00013a10: 7274 6963 6573 2e20 2042 6520 6361 7265 rtices. Be care\n+00013a20: 6675 6c20 7769 7468 2076 6572 7465 7820 ful with vertex \n+00013a30: 6f72 6465 7221 0a20 2064 6566 2072 6774 order!. def rgt\n+00013a40: 2070 6f6c 7967 6f6e 2028 7052 3129 2870 polygon (pR1)(p\n+00013a50: 5232 2928 7052 3329 2870 5234 2928 7052 R2)(pR3)(pR4)(pR\n+00013a60: 3529 0a20 2064 6566 206c 6674 2070 6f6c 5). def lft pol\n+00013a70: 7967 6f6e 2028 704c 3529 2870 4c34 2928 ygon (pL5)(pL4)(\n+00013a80: 704c 3329 2870 4c32 2928 704c 3129 0a20 pL3)(pL2)(pL1). \n+00013a90: 2064 6566 2066 7274 2070 6f6c 7967 6f6e def frt polygon\n+00013aa0: 2028 7052 3229 2870 5231 2928 704c 3129 (pR2)(pR1)(pL1)\n+00013ab0: 2870 4c32 290a 2020 6465 6620 6263 6b20 (pL2). def bck \n+00013ac0: 706f 6c79 676f 6e20 2870 5234 2928 7052 polygon (pR4)(pR\n+00013ad0: 3329 2870 4c33 2928 704c 3429 0a20 2064 3)(pL3)(pL4). d\n+00013ae0: 6566 2074 6672 2070 6f6c 7967 6f6e 2028 ef tfr polygon (\n+00013af0: 7052 3129 2870 5235 2928 704c 3529 2870 pR1)(pR5)(pL5)(p\n+00013b00: 4c31 290a 2020 6465 6620 7462 6b20 706f L1). def tbk po\n+00013b10: 6c79 676f 6e20 2870 5235 2928 7052 3429 lygon (pR5)(pR4)\n+00013b20: 2870 4c34 2928 704c 3529 0a20 2064 6566 (pL4)(pL5). def\n+00013b30: 2062 6f74 2070 6f6c 7967 6f6e 2028 7052 bot polygon (pR\n+00013b40: 3229 2870 4c32 2928 704c 3329 2870 5233 2)(pL2)(pL3)(pR3\n+00013b50: 290a 2020 6465 6620 646f 6f72 2070 6f6c ). def door pol\n+00013b60: 7967 6f6e 5b66 696c 6c63 6f6c 6f72 3d62 ygon[fillcolor=b\n+00013b70: 726f 776e 5d20 2870 4431 2928 7044 3229 rown] (pD1)(pD2)\n+00013b80: 2870 4433 2928 7044 3429 0a20 2064 6566 (pD3)(pD4). def\n+00013b90: 2068 6f75 7365 207b 207b 7267 747d 7b6c house { {rgt}{l\n+00013ba0: 6674 7d7b 6672 747d 7b62 636b 7d7b 7466 ft}{frt}{bck}{tf\n+00013bb0: 727d 7b74 626b 7d7b 626f 747d 7b64 6f6f r}{tbk}{bot}{doo\n+00013bc0: 727d 207d 0a20 2020 5469 6d65 2066 6f72 r} }. Time for\n+00013bd0: 2061 2073 616e 6974 7920 6368 6563 6b2e a sanity check.\n+00013be0: 2020 4164 6420 7468 6520 6c69 6e65 0a20 Add the line. \n+00013bf0: 207b 686f 7573 657d 0a61 6e64 2074 6869 {house}.and thi\n+00013c00: 7320 6973 2077 6861 7420 7765 2067 6574 s is what we get\n+00013c10: 2e0a 0a00 085b 696d 6167 6520 7372 633d .....[image src=\n+00013c20: 2265 7831 3330 2e70 6e67 2220 7465 7874 \"ex130.png\" text\n+00013c30: 3d22 496d 6167 6520 6578 3133 3020 6f6d =\"Image ex130 om\n+00013c40: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n+00013c50: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n+00013c60: 6375 6d65 6e74 2e22 0008 5d0a 0a54 6869 cument.\"..]..Thi\n+00013c70: 7320 6973 2063 6f72 7265 6374 2c20 6275 s is correct, bu\n+00013c80: 7420 646f 6573 206e 6f74 2072 6576 6561 t does not revea\n+00013c90: 6c20 7665 7279 206d 7563 682e 2020 436f l very much. Co\n+00013ca0: 6d6d 6f6e 2065 7272 6f72 7320 6172 650a mmon errors are.\n+00013cb0: 6d69 7370 6c61 6365 6420 7665 7274 6963 misplaced vertic\n+00013cc0: 6573 2061 6e64 2070 6f6c 7967 6f6e 7320 es and polygons \n+00013cd0: 6d69 7373 696e 6720 656e 7469 7265 6c79 missing entirely\n+00013ce0: 2064 7565 2074 6f20 696e 636f 7272 6563 due to incorrec\n+00013cf0: 7420 7665 7274 6578 0a6f 7264 6572 2e20 t vertex.order. \n+00013d00: 2054 6f20 7275 6c65 2074 6865 7365 206f To rule these o\n+00013d10: 7574 2c20 6c65 7427 7320 696e 7370 6563 ut, let's inspec\n+00013d20: 7420 616c 6c20 7369 6465 7320 6f66 2074 t all sides of t\n+00013d30: 6865 2068 6f75 7365 2e20 2054 6869 730a he house. This.\n+00013d40: 6973 206e 6f74 2068 6172 642e 2020 4d65 is not hard. Me\n+00013d50: 7265 6c79 2072 6570 6c61 6365 2074 6865 rely replace the\n+00013d60: 2072 6566 6572 656e 6365 207b 686f 7573 reference {hous\n+00013d70: 657d 2077 6974 6820 6120 e280 9872 6570 e} with a ...rep\n+00013d80: 6561 74e2 8099 2e0a 2a4e 6f74 6520 5265 eat.....*Note Re\n+00013d90: 7065 6174 733a 3a2e 0a20 2072 6570 6561 peats::.. repea\n+00013da0: 7420 7b20 3133 2c20 726f 7461 7465 2833 t { 13, rotate(3\n+00013db0: 302c 205b 312c 322c 335d 292c 2074 7261 0, [1,2,3]), tra\n+00013dc0: 6e73 6c61 7465 285b 332c 302c 305d 2920 nslate([3,0,0]) \n+00013dd0: 7d20 7b68 6f75 7365 7d0a 0008 5b69 6d61 } {house}...[ima\n+00013de0: 6765 2073 7263 3d22 6578 3134 302e 706e ge src=\"ex140.pn\n+00013df0: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+00013e00: 7831 3430 206f 6d69 7474 6564 2069 6e20 x140 omitted in \n+00013e10: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+00013e20: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+00013e30: 085d 0a0a 4167 6169 6e20 7468 696e 6773 .]..Again things\n+00013e40: 206c 6f6f 6b20 636f 7272 6563 742e 2020 look correct. \n+00013e50: 4e6f 7465 2074 6861 7420 7468 6520 6869 Note that the hi\n+00013e60: 6464 656e 2073 7572 6661 6365 2061 6c67 dden surface alg\n+00013e70: 6f72 6974 686d 0a68 616e 646c 6573 2069 orithm.handles i\n+00013e80: 6e74 6572 7365 6374 696e 6720 706f 6c79 ntersecting poly\n+00013e90: 676f 6e73 2063 6f72 7265 6374 6c79 2077 gons correctly w\n+00013ea0: 6865 7265 2073 6f6d 6520 636f 7069 6573 here some copies\n+00013eb0: 206f 6620 7468 6520 686f 7573 650a 6f76 of the house.ov\n+00013ec0: 6572 6c61 702e 0a0a 2020 204c 6574 2773 erlap... Let's\n+00013ed0: 206c 6179 206f 7574 2074 6865 2067 656f lay out the geo\n+00013ee0: 6d65 7472 7920 6f66 2070 6572 7370 6563 metry of perspec\n+00013ef0: 7469 7665 2070 726f 6a65 6374 696f 6e20 tive projection \n+00013f00: 6f66 2074 6865 2068 6f75 7365 0a6f 6e74 of the house.ont\n+00013f10: 6f20 6120 706c 616e 6520 7769 7468 2072 o a plane with r\n+00013f20: 6179 7320 7061 7373 696e 6720 7468 726f ays passing thro\n+00013f30: 7567 6820 7468 6520 6f72 6967 696e 2e20 ugh the origin. \n+00013f40: 2042 6567 696e 2062 7920 706f 7369 7469 Begin by positi\n+00013f50: 6f6e 696e 670a 7468 6520 686f 7573 6520 oning.the house \n+00013f60: 7477 656c 7665 2075 6e69 7473 2062 6163 twelve units bac\n+00013f70: 6b20 6f6e 2074 6865 206e 6567 6174 6976 k on the negativ\n+00013f80: 6520 7a2d 6178 6973 2061 6e64 2061 6464 e z-axis and add\n+00013f90: 696e 6720 6120 7365 7420 6f66 0a63 6f6f ing a set of.coo\n+00013fa0: 7264 696e 6174 6520 6178 6573 2e20 2054 rdinate axes. T\n+00013fb0: 6f20 6d6f 7665 2074 6865 2068 6f75 7365 o move the house\n+00013fc0: 2077 6520 6e65 6564 206f 6e6c 7920 6368 we need only ch\n+00013fd0: 616e 6765 2074 6865 2022 686f 7573 650a ange the \"house.\n+00013fe0: 706f 7369 7469 6f6e 696e 6722 2074 7261 positioning\" tra\n+00013ff0: 6e73 666f 726d 2064 6566 696e 6564 2065 nsform defined e\n+00014000: 6172 6c69 6572 2e0a 2020 6465 6620 6870 arlier.. def hp\n+00014010: 2072 6f74 6174 6528 2d34 302c 205b 302c rotate(-40, [0,\n+00014020: 312c 305d 2920 7468 656e 2074 7261 6e73 1,0]) then trans\n+00014030: 6c61 7465 285b 302c 302c 2d31 325d 290a late([0,0,-12]).\n+00014040: 2020 6465 6620 6178 6573 207b 0a20 2020 def axes {. \n+00014050: 2064 6566 2073 7a20 310a 2020 2020 6c69 def sz 1. li\n+00014060: 6e65 205b 6172 726f 7773 3d3c 2d3e 5d20 ne [arrows=<->] \n+00014070: 2873 7a2c 302c 3029 284f 2928 302c 737a (sz,0,0)(O)(0,sz\n+00014080: 2c30 290a 2020 2020 6c69 6e65 205b 6172 ,0). line [ar\n+00014090: 726f 7773 3d2d 3e5d 2020 284f 2928 302c rows=->] (O)(0,\n+000140a0: 302c 737a 290a 2020 2020 6c69 6e65 205b 0,sz). line [\n+000140b0: 6c69 6e65 7769 6474 683d 2e32 7074 2c6c linewidth=.2pt,l\n+000140c0: 696e 6563 6f6c 6f72 3d62 6c75 652c 6c69 inecolor=blue,li\n+000140d0: 6e65 7374 796c 653d 6461 7368 6564 5d20 nestyle=dashed] \n+000140e0: 284f 2928 302c 302c 2d31 3029 0a20 2020 (O)(0,0,-10). \n+000140f0: 2073 7065 6369 616c 207c 5c75 7075 745b special |\\uput[\n+00014100: 725d 2331 7b24 7824 7d5c 7570 7574 5b75 r]#1{$x$}\\uput[u\n+00014110: 5d23 327b 2479 247d 5c75 7075 745b 6c5d ]#2{$y$}\\uput[l]\n+00014120: 2333 7b24 7a24 7d7c 0a20 2020 2020 2028 #3{$z$}|. (\n+00014130: 737a 2c30 2c30 2928 302c 737a 2c30 2928 sz,0,0)(0,sz,0)(\n+00014140: 302c 302c 737a 290a 2020 7d0a 0a20 2020 0,0,sz). }.. \n+00014150: 5469 6d65 2066 6f72 2061 6e6f 7468 6572 Time for another\n+00014160: 2074 6573 742e 2020 4c65 7427 7320 6275 test. Let's bu\n+00014170: 696c 6420 6120 7265 616c 2076 6965 7720 ild a real view \n+00014180: 7472 616e 7366 6f72 6d2c 2063 7265 6174 transform, creat\n+00014190: 696e 6720 610a e280 9c76 6972 7475 616c ing a....virtual\n+000141a0: 2063 616d 6572 61e2 809d 2074 6f20 6c6f camera... to lo\n+000141b0: 6f6b 2061 7420 7468 6520 7363 656e 6520 ok at the scene \n+000141c0: 7765 2061 7265 2063 6f6e 7374 7275 6374 we are construct\n+000141d0: 696e 672e 2020 5265 706c 6163 6520 7468 ing. Replace th\n+000141e0: 650a e280 9872 6570 6561 74e2 8099 2077 e....repeat... w\n+000141f0: 6974 680a 2020 6465 6620 6579 6520 2831 ith. def eye (1\n+00014200: 302c 342c 3130 290a 2020 6465 6620 6c6f 0,4,10). def lo\n+00014210: 6f6b 5f61 7420 2830 2c30 2c2d 3529 0a20 ok_at (0,0,-5). \n+00014220: 2070 7574 207b 2076 6965 7728 2865 7965 put { view((eye\n+00014230: 292c 2028 6c6f 6f6b 5f61 7429 2920 7d20 ), (look_at)) } \n+00014240: 7b20 7b68 6f75 7365 7d7b 6178 6573 7d20 { {house}{axes} \n+00014250: 7d0a 2020 2054 6865 20e2 809c 7669 6577 }. The ...view\n+00014260: 2074 7261 6e73 666f 726d e280 9d20 7265 transform... re\n+00014270: 706f 7369 7469 6f6e 7320 7468 6520 7363 positions the sc\n+00014280: 656e 6520 736f 2074 6861 7420 7468 6520 ene so that the \n+00014290: 706f 696e 7420 e280 9865 7965 e280 9920 point ...eye... \n+000142a0: 6973 0a61 7420 7468 6520 6f72 6967 696e is.at the origin\n+000142b0: 2061 6e64 2074 6865 2064 6972 6563 7469 and the directi\n+000142c0: 6f6e 2066 726f 6d20 e280 9865 7965 e280 on from ...eye..\n+000142d0: 9920 746f 20e2 8098 6c6f 6f6b 5f61 74e2 . to ...look_at.\n+000142e0: 8099 2069 7320 7468 6520 6e65 6761 7469 .. is the negati\n+000142f0: 7665 0a7a 2d61 7869 732e 2020 5468 6973 ve.z-axis. This\n+00014300: 2072 6571 7569 7265 7320 6120 726f 7461 requires a rota\n+00014310: 7469 6f6e 2061 6e64 2061 2074 7261 6e73 tion and a trans\n+00014320: 6c61 7469 6f6e 2074 6861 7420 6172 6520 lation that are \n+00014330: 616c 6c20 7061 636b 6564 0a69 6e74 6f20 all packed.into \n+00014340: 7468 6520 636f 6e73 7472 7563 746f 7220 the constructor \n+00014350: e280 9876 6965 77e2 8099 2e0a 0a00 085b ...view........[\n+00014360: 696d 6167 6520 7372 633d 2265 7831 3530 image src=\"ex150\n+00014370: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n+00014380: 6520 6578 3135 3020 6f6d 6974 7465 6420 e ex150 omitted \n+00014390: 696e 2074 6578 7420 7665 7273 696f 6e20 in text version \n+000143a0: 6f66 2074 6869 7320 646f 6375 6d65 6e74 of this document\n+000143b0: 2e22 0008 5d0a 0a54 6869 7320 6973 2073 .\"..]..This is s\n+000143c0: 7461 7274 696e 6720 746f 206c 6f6f 6b20 tarting to look \n+000143d0: 676f 6f64 2120 2041 6464 2074 6865 2070 good! Add the p\n+000143e0: 726f 6a65 6374 696f 6e20 706c 616e 6520 rojection plane \n+000143f0: 6861 6c66 2077 6179 0a62 6574 7765 656e half way.between\n+00014400: 2074 6865 206f 7269 6769 6e20 616e 6420 the origin and \n+00014410: 7468 6520 686f 7573 6520 6174 207a 3d2d the house at z=-\n+00014420: 352e 2020 5765 276c 6c20 7472 7920 7468 5. We'll try th\n+00014430: 6520 616e 676c 6520 6172 6775 6d65 6e74 e angle argument\n+00014440: 0a66 6561 7475 7265 206f 6620 e280 9873 .feature of ...s\n+00014450: 7065 6369 616c e280 9920 746f 2070 6f73 pecial... to pos\n+00014460: 6974 696f 6e20 6120 6c61 6265 6c2e 0a20 ition a label.. \n+00014470: 2064 6566 2070 2035 2025 2070 726f 6a65 def p 5 % proje\n+00014480: 6374 696f 6e20 6469 7374 616e 6365 2028 ction distance (\n+00014490: 706c 616e 6520 6174 207a 3d2d 7029 0a20 plane at z=-p). \n+000144a0: 2064 6566 2070 726f 6a65 6374 696f 6e5f def projection_\n+000144b0: 706c 616e 6520 7b0a 2020 2020 6465 6620 plane {. def \n+000144c0: 737a 2031 2e35 0a20 2020 2070 6f6c 7967 sz 1.5. polyg\n+000144d0: 6f6e 2028 2d73 7a2c 2d73 7a2c 2d70 2928 on (-sz,-sz,-p)(\n+000144e0: 737a 2c2d 737a 2c2d 7029 2873 7a2c 737a sz,-sz,-p)(sz,sz\n+000144f0: 2c2d 7029 282d 737a 2c73 7a2c 2d70 290a ,-p)(-sz,sz,-p).\n+00014500: 2020 2020 7370 6563 6961 6c20 7c5c 7270 special |\\rp\n+00014510: 7574 5b62 5d23 312d 3223 337b 5c66 6f6f ut[b]#1-2#3{\\foo\n+00014520: 746e 6f74 6573 697a 655c 7366 2070 726f tnotesize\\sf pro\n+00014530: 6a65 6374 696f 6e20 706c 616e 657d 7c20 jection plane}| \n+00014540: 0a20 2020 2020 2028 2d73 7a2c 2d73 7a2c . (-sz,-sz,\n+00014550: 2d70 2928 737a 2c2d 737a 2c2d 7029 2830 -p)(sz,-sz,-p)(0\n+00014560: 2c2d 737a 2b2e 312c 2d70 290a 2020 7d0a ,-sz+.1,-p). }.\n+00014570: 4164 6420 7b70 726f 6a65 6374 696f 6e5f Add {projection_\n+00014580: 706c 616e 657d 2074 6f20 7468 6520 6c69 plane} to the li\n+00014590: 7374 206f 6620 6f62 6a65 6374 7320 696e st of objects in\n+000145a0: 2074 6865 20e2 8098 7075 74e2 8099 2061 the ...put... a\n+000145b0: 626f 7665 2e0a 0a00 085b 696d 6167 6520 bove.....[image \n+000145c0: 7372 633d 2265 7831 3630 2e70 6e67 2220 src=\"ex160.png\" \n+000145d0: 7465 7874 3d22 496d 6167 6520 6578 3136 text=\"Image ex16\n+000145e0: 3020 6f6d 6974 7465 6420 696e 2074 6578 0 omitted in tex\n+000145f0: 7420 7665 7273 696f 6e20 6f66 2074 6869 t version of thi\n+00014600: 7320 646f 6375 6d65 6e74 2e22 0008 5d0a s document.\"..].\n+00014610: 0a20 2020 5468 6520 7761 7920 7765 2063 . The way we c\n+00014620: 6f6e 7374 7275 6374 6564 2074 6865 2070 onstructed the p\n+00014630: 6f69 6e74 7320 6f66 2074 6865 2068 6f75 oints of the hou\n+00014640: 7365 206e 6f77 206d 616b 6573 2069 7420 se now makes it \n+00014650: 6561 7379 2074 6f0a 6472 6177 2072 6179 easy to.draw ray\n+00014660: 7320 6f66 2070 726f 6a65 6374 696f 6e2e s of projection.\n+00014670: 2020 5765 276c 6c20 6361 7374 206f 6e65 We'll cast one\n+00014680: 2072 6179 2066 726f 6d20 6576 6572 7920 ray from every \n+00014690: 7669 7369 626c 6520 7665 7274 6578 0a6f visible vertex.o\n+000146a0: 6620 7468 6520 686f 7573 6520 616e 6420 f the house and \n+000146b0: 6465 6669 6e65 206f 7074 696f 6e73 2073 define options s\n+000146c0: 6f20 7468 6520 6170 7065 6172 616e 6365 o the appearance\n+000146d0: 206f 6620 616c 6c20 7261 7973 2063 616e of all rays can\n+000146e0: 2062 650a 6368 616e 6765 6420 6174 2074 be.changed at t\n+000146f0: 6865 2073 616d 6520 7469 6d65 2e0a 2020 he same time.. \n+00014700: 6465 6620 7072 6f6a 6563 7469 6f6e 5f72 def projection_r\n+00014710: 6179 7320 7b0a 2020 2020 6465 6620 7261 ays {. def ra\n+00014720: 796f 7074 205b 6c69 6e65 7769 6474 683d yopt [linewidth=\n+00014730: 2e33 7074 2c6c 696e 6563 6f6c 6f72 3d6c .3pt,linecolor=l\n+00014740: 6967 6874 6772 6179 5d0a 2020 2020 6c69 ightgray]. li\n+00014750: 6e65 205b 7261 796f 7074 5d28 4f29 2870 ne [rayopt](O)(p\n+00014760: 5231 2920 6c69 6e65 205b 7261 796f 7074 R1) line [rayopt\n+00014770: 5d28 4f29 2870 5232 2920 6c69 6e65 5b72 ](O)(pR2) line[r\n+00014780: 6179 6f70 745d 284f 2928 7052 3329 0a20 ayopt](O)(pR3). \n+00014790: 2020 206c 696e 6520 5b72 6179 6f70 745d line [rayopt]\n+000147a0: 284f 2928 7052 3429 206c 696e 6520 5b72 (O)(pR4) line [r\n+000147b0: 6179 6f70 745d 284f 2928 7052 3529 0a20 ayopt](O)(pR5). \n+000147c0: 2020 206c 696e 6520 5b72 6179 6f70 745d line [rayopt]\n+000147d0: 284f 2928 704c 3129 206c 696e 6520 5b72 (O)(pL1) line [r\n+000147e0: 6179 6f70 745d 284f 2928 704c 3229 206c ayopt](O)(pL2) l\n+000147f0: 696e 655b 7261 796f 7074 5d28 4f29 2870 ine[rayopt](O)(p\n+00014800: 4c35 290a 2020 2020 6c69 6e65 205b 7261 L5). line [ra\n+00014810: 796f 7074 5d28 4f29 2870 4431 2920 6c69 yopt](O)(pD1) li\n+00014820: 6e65 205b 7261 796f 7074 5d28 4f29 2870 ne [rayopt](O)(p\n+00014830: 4432 2920 0a20 2020 206c 696e 6520 5b72 D2) . line [r\n+00014840: 6179 6f70 745d 284f 2928 7044 3329 206c ayopt](O)(pD3) l\n+00014850: 696e 6520 5b72 6179 6f70 745d 284f 2928 ine [rayopt](O)(\n+00014860: 7044 3429 200a 2020 7d0a 5468 6520 7265 pD4) . }.The re\n+00014870: 7375 6c74 2069 7320 7368 6f77 6e20 6865 sult is shown he\n+00014880: 7265 2e0a 0a00 085b 696d 6167 6520 7372 re.....[image sr\n+00014890: 633d 2265 7831 3730 2e70 6e67 2220 7465 c=\"ex170.png\" te\n+000148a0: 7874 3d22 496d 6167 6520 6578 3137 3020 xt=\"Image ex170 \n+000148b0: 6f6d 6974 7465 6420 696e 2074 6578 7420 omitted in text \n+000148c0: 7665 7273 696f 6e20 6f66 2074 6869 7320 version of this \n+000148d0: 646f 6375 6d65 6e74 2e22 0008 5d0a 0a54 document.\"..]..T\n+000148e0: 6865 2072 6179 7320 7069 6572 6365 2074 he rays pierce t\n+000148f0: 6865 2070 726f 6a65 6374 696f 6e20 706c he projection pl\n+00014900: 616e 6520 6174 2074 6865 2063 6f72 7265 ane at the corre\n+00014910: 7370 6f6e 6469 6e67 2070 6f69 6e74 7320 sponding points \n+00014920: 6f6e 2074 6865 0a70 6572 7370 6563 7469 on the.perspecti\n+00014930: 7665 2069 6d61 6765 2077 6520 6172 6520 ve image we are \n+00014940: 7472 7969 6e67 2074 6f20 6472 6177 2e20 trying to draw. \n+00014950: 2041 6c62 7265 6368 7420 44c3 bc72 6572 Albrecht D..rer\n+00014960: 2061 6e64 2068 6973 0a52 656e 6169 7373 and his.Renaiss\n+00014970: 616e 6365 2063 6f6e 7465 6d70 6f72 6172 ance contemporar\n+00014980: 6965 7320 6861 6420 7468 6520 7361 6d65 ies had the same\n+00014990: 2069 6465 6120 696e 2074 6865 2065 6172 idea in the ear\n+000149a0: 6c79 2031 3530 3027 732e 0a0a 0008 5b69 ly 1500's.....[i\n+000149b0: 6d61 6765 2073 7263 3d22 6475 6572 6572 mage src=\"duerer\n+000149c0: 2e70 6e67 2220 7465 7874 3d22 496d 6167 .png\" text=\"Imag\n+000149d0: 6520 6f66 2044 7565 7265 7227 7320 7065 e of Duerer's pe\n+000149e0: 7273 7065 6374 6976 6520 636f 6d70 7574 rspective comput\n+000149f0: 6572 206f 6d69 7474 6564 2069 6e20 7465 er omitted in te\n+00014a00: 7874 2076 6572 7369 6f6e 206f 6620 7468 xt version of th\n+00014a10: 6973 2064 6f63 756d 656e 742e 2200 085d is document.\"..]\n+00014a20: 0a0a 2020 2041 6c6c 2074 6861 7427 7320 .. All that's \n+00014a30: 6c65 6674 2069 7320 746f 2066 696e 6420 left is to find \n+00014a40: 6120 7761 7920 746f 2063 6f6e 6e65 6374 a way to connect\n+00014a50: 2074 6865 2070 6f69 6e74 7320 6f66 2074 the points of t\n+00014a60: 6865 2068 6f75 7365 0a6f 6e20 7468 6520 he house.on the \n+00014a70: 7072 6f6a 6563 7469 6f6e 2070 6c61 6e65 projection plane\n+00014a80: 2e20 2057 6520 636f 756c 6420 7075 6c6c . We could pull\n+00014a90: 206f 7574 2061 2067 6f6f 6420 636f 6d70 out a good comp\n+00014aa0: 7574 6572 2067 7261 7068 6963 730a 7465 uter graphics.te\n+00014ab0: 7874 2c20 6669 6e64 2074 6865 206e 6563 xt, find the nec\n+00014ac0: 6573 7361 7279 206d 6174 7269 782c 2061 essary matrix, a\n+00014ad0: 6e64 2065 6e74 6572 2069 7420 6f75 7273 nd enter it ours\n+00014ae0: 656c 7665 7320 6173 2061 2074 7261 6e73 elves as a trans\n+00014af0: 666f 726d 0a6c 6974 6572 616c 2e20 202a form.literal. *\n+00014b00: 4e6f 7465 2054 7261 6e73 666f 726d 206c Note Transform l\n+00014b10: 6974 6572 616c 733a 3a2e 2020 5468 6174 iterals::. That\n+00014b20: 2077 6f72 6b20 6973 2061 6c72 6561 6479 work is already\n+00014b30: 2064 6f6e 652c 0a68 6f77 6576 6572 2e20 done,.however. \n+00014b40: 2057 6520 6361 6e20 7573 6520 7468 6520 We can use the \n+00014b50: e280 9870 726f 6a65 6374 2870 29e2 8099 ...project(p)...\n+00014b60: 2063 6f6e 7374 7275 6374 6f72 2e0a 0a20 constructor... \n+00014b70: 2020 5468 6572 6520 6172 6520 7374 696c There are stil\n+00014b80: 6c20 736f 6d65 2064 6574 6169 6c73 2074 l some details t\n+00014b90: 6861 7420 7265 7175 6972 6520 6361 7265 hat require care\n+00014ba0: 2e20 2050 726f 6a65 6374 696f 6e20 7769 . Projection wi\n+00014bb0: 6c6c 0a66 6c61 7474 656e 2077 6861 7465 ll.flatten whate\n+00014bc0: 7665 7220 6973 2074 7261 6e73 666f 726d ver is transform\n+00014bd0: 6564 206f 6e74 6f20 7468 6520 706c 616e ed onto the plan\n+00014be0: 6520 7a3d 2d70 2e20 2054 6865 7265 666f e z=-p. Therefo\n+00014bf0: 7265 2061 6e79 2070 6172 740a 6f66 2074 re any part.of t\n+00014c00: 6865 2068 6f75 7365 2063 6f75 6c64 2064 he house could d\n+00014c10: 6973 6170 7065 6172 2062 6568 696e 6420 isappear behind \n+00014c20: 7468 6520 7072 6f6a 6563 7469 6f6e 2070 the projection p\n+00014c30: 6c61 6e65 2028 7468 6520 6869 6464 656e lane (the hidden\n+00014c40: 0a73 7572 6661 6365 2061 6c67 6f72 6974 .surface algorit\n+00014c50: 686d 206f 7264 6572 7320 6f62 6a65 6374 hm orders object\n+00014c60: 7320 6174 2074 6865 2073 616d 6520 6465 s at the same de\n+00014c70: 7074 6820 6172 6269 7472 6172 696c 7929 pth arbitrarily)\n+00014c80: 2e20 2054 6865 0a64 6f6f 7220 6d61 7920 . The.door may \n+00014c90: 616c 736f 2064 6973 6170 7065 6172 2062 also disappear b\n+00014ca0: 6568 696e 6420 7468 6520 6672 6f6e 7420 ehind the front \n+00014cb0: 6f66 2074 6865 2068 6f75 7365 2e20 2054 of the house. T\n+00014cc0: 6f20 6d61 6b65 2073 7572 650a 6576 6572 o make sure.ever\n+00014cd0: 7974 6869 6e67 2072 656d 6169 6e73 2076 ything remains v\n+00014ce0: 6973 6962 6c65 2c20 7765 276c 6c20 706c isible, we'll pl\n+00014cf0: 6163 6520 7468 6520 686f 7573 6520 6120 ace the house a \n+00014d00: 7469 6e79 2062 6974 2069 6e20 6672 6f6e tiny bit in fron\n+00014d10: 7420 6f66 0a74 6865 2070 726f 6a65 6374 t of.the project\n+00014d20: 696f 6e20 706c 616e 6520 616e 6420 6120 ion plane and a \n+00014d30: 7365 636f 6e64 2063 6f70 7920 6f66 2074 second copy of t\n+00014d40: 6865 2064 6f6f 7220 696e 2066 726f 6e74 he door in front\n+00014d50: 206f 6620 7468 650a 686f 7573 652e 0a20 of the.house.. \n+00014d60: 2064 6566 2070 726f 6a65 6374 696f 6e20 def projection \n+00014d70: 7b0a 2020 2020 2520 6520 6973 2061 2073 {. % e is a s\n+00014d80: 6d61 6c6c 206e 756d 6265 7220 6465 6669 mall number defi\n+00014d90: 6e65 6420 6162 6f76 650a 2020 2020 7075 ned above. pu\n+00014da0: 7420 7b20 7072 6f6a 6563 7428 7029 2074 t { project(p) t\n+00014db0: 6865 6e20 7472 616e 736c 6174 6528 5b30 hen translate([0\n+00014dc0: 2c30 2c31 2a65 5d29 207d 207b 686f 7573 ,0,1*e]) } {hous\n+00014dd0: 657d 0a20 2020 2070 7574 207b 2070 726f e}. put { pro\n+00014de0: 6a65 6374 2870 2920 7468 656e 2074 7261 ject(p) then tra\n+00014df0: 6e73 6c61 7465 285b 302c 302c 322a 655d nslate([0,0,2*e]\n+00014e00: 2920 7d20 7b64 6f6f 727d 0a20 207d 0a0a ) } {door}. }..\n+00014e10: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n+00014e20: 3138 302e 706e 6722 2074 6578 743d 2249 180.png\" text=\"I\n+00014e30: 6d61 6765 2065 7831 3830 206f 6d69 7474 mage ex180 omitt\n+00014e40: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n+00014e50: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n+00014e60: 656e 742e 2200 085d 0a0a 2020 2049 6620 ent.\"..].. If \n+00014e70: 796f 7520 6861 7665 2073 7475 6469 6564 you have studied\n+00014e80: 2061 6e64 2075 6e64 6572 7374 616e 6420 and understand \n+00014e90: 616c 6c20 7468 6973 2c20 796f 7520 6172 all this, you ar\n+00014ea0: 6520 7765 6c6c 206f 6e20 7468 6520 7761 e well on the wa\n+00014eb0: 790a 746f 2073 7563 6365 7373 2077 6974 y.to success wit\n+00014ec0: 6820 e280 9873 6b65 7463 68e2 8099 2e20 h ...sketch.... \n+00014ed0: 204e 6f74 2073 686f 776e 2061 7265 2074 Not shown are t\n+00014ee0: 6865 2032 3020 6f72 2073 6f20 6974 6572 he 20 or so iter\n+00014ef0: 6174 696f 6e73 2074 6861 740a 7765 7265 ations that.were\n+00014f00: 2072 6571 7569 7265 6420 746f 2066 696e required to fin\n+00014f10: 6420 6120 7265 6173 6f6e 6162 6c65 2076 d a reasonable v\n+00014f20: 6965 7769 6e67 2061 6e67 6c65 2061 6e64 iewing angle and\n+00014f30: 2068 6f75 7365 2070 6f73 6974 696f 6e2c house position,\n+00014f40: 0a65 7463 2e20 204e 6f6e 6574 6865 6c65 .etc. Nonethele\n+00014f50: 7373 2c20 7468 6973 2064 7261 7769 6e67 ss, this drawing\n+00014f60: 2077 6173 2063 6f6d 706c 6574 6564 2069 was completed i\n+00014f70: 6e20 6162 6f75 7420 616e 2068 6f75 722e n about an hour.\n+00014f80: 2020 5768 696c 6520 610a 4755 4920 746f While a.GUI to\n+00014f90: 6f6c 206d 6179 2068 6176 6520 6265 656e ol may have been\n+00014fa0: 2061 206c 6974 746c 6520 6661 7374 6572 a little faster\n+00014fb0: 2c20 6974 2069 7320 756e 6c69 6b65 6c79 , it is unlikely\n+00014fc0: 2074 6861 7420 6120 6e65 770a 6472 6177 that a new.draw\n+00014fd0: 696e 672c 2069 7473 656c 6620 6120 7065 ing, itself a pe\n+00014fe0: 7273 7065 6374 6976 6520 7072 6f6a 6563 rspective projec\n+00014ff0: 7469 6f6e 206f 6620 7468 6520 7363 656e tion of the scen\n+00015000: 652c 2063 6f75 6c64 2062 650a 6765 6e65 e, could be.gene\n+00015010: 7261 7465 6420 7769 7468 2074 776f 206d rated with two m\n+00015020: 6f72 6520 6d69 6e75 7465 7327 2077 6f72 ore minutes' wor\n+00015030: 6b21 2020 4a75 7374 2063 6861 6e67 6520 k! Just change \n+00015040: 7468 6520 7669 6577 2074 7261 6e73 666f the view transfo\n+00015050: 726d 0a74 6f0a 2020 7075 7420 7b20 7669 rm.to. put { vi\n+00015060: 6577 2828 6579 6529 2c20 286c 6f6f 6b5f ew((eye), (look_\n+00015070: 6174 2929 2074 6865 6e20 7065 7273 7065 at)) then perspe\n+00015080: 6374 6976 6528 3929 207d 207b 202e 2e2e ctive(9) } { ...\n+00015090: 0a61 6e64 2070 726f 6475 6365 2074 6869 .and produce thi\n+000150a0: 732e 0a0a 0008 5b69 6d61 6765 2073 7263 s.....[image src\n+000150b0: 3d22 6578 3139 302e 706e 6722 2074 6578 =\"ex190.png\" tex\n+000150c0: 743d 2249 6d61 6765 2065 7831 3930 206f t=\"Image ex190 o\n+000150d0: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n+000150e0: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n+000150f0: 6f63 756d 656e 742e 2200 085d 0a0a 1f0a ocument.\"..]....\n+00015100: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n+00015110: 6f2c 2020 4e6f 6465 3a20 4120 7465 6368 o, Node: A tech\n+00015120: 6e69 6361 6c20 6472 6177 696e 672c 2020 nical drawing, \n+00015130: 4e65 7874 3a20 4120 6869 6572 6172 6368 Next: A hierarch\n+00015140: 6963 616c 206d 6f64 656c 2c20 2050 7265 ical model, Pre\n+00015150: 763a 204f 7665 7276 6965 772c 2020 5570 v: Overview, Up\n+00015160: 3a20 4275 696c 6469 6e67 2061 2064 7261 : Building a dra\n+00015170: 7769 6e67 0a0a 342e 3220 4120 7465 6368 wing..4.2 A tech\n+00015180: 6e69 6361 6c20 6472 6177 696e 670a 3d3d nical drawing.==\n 00015190: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-000151a0: 3d3d 3d3d 3d3d 3d0a 0a4c 6574 2773 206c =======..Let's l\n-000151b0: 6f6f 6b20 6174 2061 2064 7261 7769 6e67 ook at a drawing\n-000151c0: 2074 6861 7420 7265 7072 6573 656e 7473 that represents\n-000151d0: 2074 6865 206b 696e 6420 6f66 2070 726f the kind of pro\n-000151e0: 626c 656d 20e2 8098 736b 6574 6368 e280 blem ...sketch..\n-000151f0: 9920 7761 730a 6d65 616e 7420 746f 2073 . was.meant to s\n-00015200: 6f6c 7665 2d2d 6120 7061 6972 206f 6620 olve--a pair of \n-00015210: 7465 7874 626f 6f6b 2066 6967 7572 6573 textbook figures\n-00015220: 2072 6567 6172 6469 6e67 2061 2070 6f6c regarding a pol\n-00015230: 7967 6f6e 616c 0a61 7070 726f 7869 6d61 ygonal.approxima\n-00015240: 7469 6f6e 206f 6620 6120 7472 756e 6361 tion of a trunca\n-00015250: 7465 6420 636f 6e65 2e20 2048 6572 6520 ted cone. Here \n-00015260: 6172 6520 7468 6520 7069 6374 7572 6573 are the pictures\n-00015270: 2077 6520 7769 6c6c 0a70 726f 6475 6365 we will.produce\n-00015280: 2e0a 0a00 085b 696d 6167 6520 7372 633d .....[image src=\n-00015290: 2265 7832 3530 2e70 6e67 2220 7465 7874 \"ex250.png\" text\n-000152a0: 3d22 496d 6167 6520 6578 3235 3020 6f6d =\"Image ex250 om\n-000152b0: 6974 7465 6420 696e 2074 6578 7420 7665 itted in text ve\n-000152c0: 7273 696f 6e20 6f66 2074 6869 7320 646f rsion of this do\n-000152d0: 6375 6d65 6e74 2e22 0008 5d20 2020 2020 cument.\"..] \n-000152e0: 0008 5b69 6d61 6765 2073 7263 3d22 6578 ..[image src=\"ex\n-000152f0: 3236 302e 706e 6722 2074 6578 743d 2249 260.png\" text=\"I\n-00015300: 6d61 6765 2065 7832 3630 206f 6d69 7474 mage ex260 omitt\n-00015310: 6564 2069 6e20 7465 7874 2076 6572 7369 ed in text versi\n-00015320: 6f6e 206f 6620 7468 6973 2064 6f63 756d on of this docum\n-00015330: 656e 742e 2200 085d 0a0a 2020 2054 6865 ent.\"..].. The\n-00015340: 2063 6f6e 6520 7368 6170 6520 6973 206a cone shape is j\n-00015350: 7573 7420 6120 7377 6570 7420 6c69 6e65 ust a swept line\n-00015360: 2077 6974 6820 6e6f 2063 6c6f 7375 7265 with no closure\n-00015370: 2074 6167 2061 6e64 2063 756c 6c69 6e67 tag and culling\n-00015380: 0a74 7572 6e65 6420 6f66 662e 2020 4265 .turned off. Be\n-00015390: 6769 6e20 6279 2073 6574 7469 6e67 2075 gin by setting u\n-000153a0: 7020 736f 6d65 2075 7365 6675 6c20 636f p some useful co\n-000153b0: 6e73 7461 6e74 732e 0a20 2064 6566 204f nstants.. def O\n-000153c0: 2028 302c 302c 3029 2064 6566 2049 205b (0,0,0) def I [\n-000153d0: 312c 302c 305d 2064 6566 204a 205b 302c 1,0,0] def J [0,\n-000153e0: 312c 305d 2064 6566 204b 205b 302c 302c 1,0] def K [0,0,\n-000153f0: 315d 0a20 2064 6566 2070 3020 2831 2c32 1]. def p0 (1,2\n-00015400: 2920 6465 6620 7031 2028 312e 352c 3029 ) def p1 (1.5,0)\n-00015410: 2064 6566 204e 2038 0a20 2064 6566 2073 def N 8. def s\n-00015420: 6567 5f72 6f74 2072 6f74 6174 6528 3336 eg_rot rotate(36\n-00015430: 3020 2f20 4e2c 205b 4a5d 290a 5468 6520 0 / N, [J]).The \n-00015440: 706f 696e 7473 20e2 8098 7030 e280 9920 points ...p0... \n-00015450: 616e 6420 e280 9870 31e2 8099 2061 7265 and ...p1... are\n-00015460: 2074 6865 2065 6e64 2070 6f69 6e74 7320 the end points \n-00015470: 6f66 2074 6865 206c 696e 6520 746f 2062 of the line to b\n-00015480: 6520 7377 6570 742e 0a54 6865 2064 6566 e swept..The def\n-00015490: 696e 6974 696f 6e20 e280 9873 6567 5f72 inition ...seg_r\n-000154a0: 6f74 e280 9920 6973 2074 6865 2073 7765 ot... is the swe\n-000154b0: 6570 2074 7261 6e73 666f 726d 6174 696f ep transformatio\n-000154c0: 6e2e 2020 5769 7468 2074 6865 7365 2c20 n. With these, \n-000154d0: 7468 650a 636f 6e65 2069 7473 656c 6620 the.cone itself \n-000154e0: 6973 2073 696d 706c 652e 0a20 2073 7765 is simple.. swe\n-000154f0: 6570 5b63 756c 6c3d 6661 6c73 655d 207b ep[cull=false] {\n-00015500: 204e 2c20 5b5b 7365 675f 726f 745d 5d20 N, [[seg_rot]] \n-00015510: 7d20 6c69 6e65 2870 3029 2870 3129 0a0a } line(p0)(p1)..\n-00015520: 2020 2054 6865 2061 7865 7320 6172 6520 The axes are \n-00015530: 6e65 7874 2061 6e64 2069 6e63 6c75 6465 next and include\n-00015540: 2061 6e20 696e 7465 7265 7369 6e67 2074 an interesing t\n-00015550: 7269 636b 2074 6861 7420 7368 6f77 7320 rick that shows \n-00015560: 7468 650a 6869 6464 656e 2070 6172 7473 the.hidden parts\n-00015570: 2061 7320 646f 7474 6564 206c 696e 6573 as dotted lines\n-00015580: 2e20 2054 6865 2073 6563 7265 7420 6973 . The secret is\n-00015590: 2064 7261 7720 7468 6520 6178 6573 2074 draw the axes t\n-000155a0: 7769 6365 2d2d 736f 6c69 640a 6c69 6e65 wice--solid.line\n-000155b0: 7320 7769 7468 2074 6865 206e 6f72 6d61 s with the norma\n-000155c0: 6c20 6869 6464 656e 2073 7572 6661 6365 l hidden surface\n-000155d0: 2061 6c67 6f72 6974 686d 2069 6e20 6566 algorithm in ef\n-000155e0: 6665 6374 2c20 616e 6420 7468 656e 0a64 fect, and then.d\n-000155f0: 6f74 7465 6420 7769 7468 2074 6865 206f otted with the o\n-00015600: 7074 696f 6e20 e280 986c 6179 3d6f 7665 ption ...lay=ove\n-00015610: 72e2 8099 2073 6f20 7468 6174 206e 6f20 r... so that no \n-00015620: 706f 6c79 676f 6e73 2063 616e 2068 6964 polygons can hid\n-00015630: 6520 7468 656d 2e0a 2020 6465 6620 6178 e them.. def ax\n-00015640: 2028 6478 2c30 2c30 2920 2520 7469 7073 (dx,0,0) % tips\n-00015650: 206f 6620 7468 6520 6178 6573 0a20 2064 of the axes. d\n-00015660: 6566 2061 7920 2830 2c64 792c 3029 0a20 ef ay (0,dy,0). \n-00015670: 2064 6566 2061 7a20 2830 2c30 2c64 7a29 def az (0,0,dz)\n-00015680: 0a20 206c 696e 655b 6172 726f 7773 3d3c . line[arrows=<\n-00015690: 2d3e 2c6c 696e 6577 6964 7468 3d2e 3470 ->,linewidth=.4p\n-000156a0: 745d 2861 7829 284f 2928 6179 290a 2020 t](ax)(O)(ay). \n-000156b0: 6c69 6e65 5b61 7272 6f77 733d 2d3e 2c6c line[arrows=->,l\n-000156c0: 696e 6577 6964 7468 3d2e 3470 745d 284f inewidth=.4pt](O\n-000156d0: 2928 617a 290a 2020 2520 7265 7065 6174 )(az). % repeat\n-000156e0: 2064 6f74 7465 6420 6173 2061 6e20 6f76 dotted as an ov\n-000156f0: 6572 6c61 7920 746f 2068 696e 7420 6174 erlay to hint at\n-00015700: 2074 6865 2068 6964 6465 6e20 6c69 6e65 the hidden line\n-00015710: 730a 2020 6c69 6e65 5b6c 6179 3d6f 7665 s. line[lay=ove\n-00015720: 722c 6c69 6e65 7374 796c 653d 646f 7474 r,linestyle=dott\n-00015730: 6564 2c6c 696e 6577 6964 7468 3d2e 3470 ed,linewidth=.4p\n-00015740: 745d 2861 7829 284f 2928 6179 290a 2020 t](ax)(O)(ay). \n-00015750: 6c69 6e65 5b6c 6179 3d6f 7665 722c 6c69 line[lay=over,li\n-00015760: 6e65 7374 796c 653d 646f 7474 6564 2c6c nestyle=dotted,l\n-00015770: 696e 6577 6964 7468 3d2e 3470 745d 284f inewidth=.4pt](O\n-00015780: 2928 617a 290a 2020 7370 6563 6961 6c7c )(az). special|\n-00015790: 5c66 6f6f 746e 6f74 6573 697a 650a 2020 \\footnotesize. \n-000157a0: 2020 2020 2020 2020 5c75 7075 745b 645d \\uput[d]\n-000157b0: 2331 7b24 7824 7d5c 7570 7574 5b75 5d23 #1{$x$}\\uput[u]#\n-000157c0: 327b 2479 247d 5c75 7075 745b 6c5d 2333 2{$y$}\\uput[l]#3\n-000157d0: 7b24 7a24 7d7c 0a20 2020 2028 6178 2928 {$z$}|. (ax)(\n-000157e0: 6179 2928 617a 290a 5468 6520 6c61 6265 ay)(az).The labe\n-000157f0: 6c73 2061 7265 2061 7070 6c69 6564 2077 ls are applied w\n-00015800: 6974 6820 e280 9850 5354 7269 636b 73e2 ith ...PSTricks.\n-00015810: 8099 2073 7065 6369 616c 206f 626a 6563 .. special objec\n-00015820: 7473 2061 7320 7573 7561 6c2e 0a0a 2020 ts as usual... \n-00015830: 2046 6f72 2074 6865 2068 6569 6768 7420 For the height \n-00015840: 6469 6d65 6e73 696f 6e20 6d61 726b 2c20 dimension mark, \n-00015850: 7468 6520 706f 7765 7220 6f66 2061 6666 the power of aff\n-00015860: 696e 6520 6172 6974 6865 7469 6320 6973 ine arithetic is\n-00015870: 2076 6572 790a 6865 6c70 6675 6c2e 0a20 very.helpful.. \n-00015880: 2064 6566 2068 6469 6d5f 7265 6620 756e def hdim_ref un\n-00015890: 6974 2828 7031 2920 2d20 284f 2929 2074 it((p1) - (O)) t\n-000158a0: 6865 6e20 5b5b 7365 675f 726f 745d 5d5e hen [[seg_rot]]^\n-000158b0: 320a 2020 6465 6620 6330 2028 7030 2920 2. def c0 (p0) \n-000158c0: 7468 656e 2073 6361 6c65 285b 4a5d 290a then scale([J]).\n-000158d0: 2020 6465 6620 6830 3020 2863 3029 202b def h00 (c0) +\n-000158e0: 2031 2e31 202a 205b 6864 696d 5f72 6566 1.1 * [hdim_ref\n-000158f0: 5d0a 2020 6465 6620 6830 3120 2863 3029 ]. def h01 (c0)\n-00015900: 202b 2031 2e39 202a 205b 6864 696d 5f72 + 1.9 * [hdim_r\n-00015910: 6566 5d0a 2020 6465 6620 6830 3220 2863 ef]. def h02 (c\n-00015920: 3029 202b 2031 2e38 202a 205b 6864 696d 0) + 1.8 * [hdim\n-00015930: 5f72 6566 5d0a 2020 6c69 6e65 2868 3030 _ref]. line(h00\n-00015940: 2928 6830 3129 0a20 2064 6566 2068 3130 )(h01). def h10\n-00015950: 2028 4f29 202b 2031 2e36 202a 205b 6864 (O) + 1.6 * [hd\n-00015960: 696d 5f72 6566 5d0a 2020 6465 6620 6831 im_ref]. def h1\n-00015970: 3120 284f 2920 2b20 312e 3920 2a20 5b68 1 (O) + 1.9 * [h\n-00015980: 6469 6d5f 7265 665d 0a20 2064 6566 2068 dim_ref]. def h\n-00015990: 3132 2028 4f29 202b 2031 2e38 202a 205b 12 (O) + 1.8 * [\n-000159a0: 6864 696d 5f72 6566 5d0a 2020 6c69 6e65 hdim_ref]. line\n-000159b0: 2868 3130 2928 6831 3129 0a20 206c 696e (h10)(h11). lin\n-000159c0: 655b 6172 726f 7773 3d3c 2d3e 5d28 6830 e[arrows=<->](h0\n-000159d0: 3229 2868 3132 290a 2020 6465 6620 686d 2)(h12). def hm\n-000159e0: 3220 2828 6830 3229 202d 2028 4f29 202b 2 ((h02) - (O) +\n-000159f0: 2028 6831 3229 202d 2028 4f29 2920 2f20 (h12) - (O)) / \n-00015a00: 3220 2b20 284f 290a 2020 7370 6563 6961 2 + (O). specia\n-00015a10: 6c7c 5c66 6f6f 746e 6f74 6573 697a 655c l|\\footnotesize\\\n-00015a20: 7270 7574 2a23 317b 2468 247d 7c28 686d rput*#1{$h$}|(hm\n-00015a30: 3229 0a20 2020 5468 6520 6765 6e65 7261 2). The genera\n-00015a40: 6c20 6964 6561 2065 6d70 6c6f 7965 6420 l idea employed \n-00015a50: 6865 7265 2069 7320 746f 2063 6f6d 7075 here is to compu\n-00015a60: 7465 2061 2075 6e69 7420 2272 6566 6572 te a unit \"refer\n-00015a70: 656e 6365 0a76 6563 746f 7222 2070 6172 ence.vector\" par\n-00015a80: 616c 6c65 6c20 746f 2074 6865 2078 7a2d allel to the xz-\n-00015a90: 706c 616e 6520 696e 2074 6865 2064 6573 plane in the des\n-00015aa0: 6972 6564 2064 6972 6563 7469 6f6e 206f ired direction o\n-00015ab0: 6620 7468 650a 6469 6d65 6e73 696f 6e20 f the.dimension \n-00015ac0: 6672 6f6d 2074 6865 206f 7269 6769 6e2e from the origin.\n-00015ad0: 2020 5468 6520 7472 616e 7366 6f72 6d61 The transforma\n-00015ae0: 7469 6f6e 20e2 8098 5b5b 7365 675f 726f tion ...[[seg_ro\n-00015af0: 745d 5d5e 32e2 8099 2072 6f74 6174 6573 t]]^2... rotates\n-00015b00: 0a74 776f 2073 6567 6d65 6e74 7320 6162 .two segments ab\n-00015b10: 6f75 7420 7468 6520 792d 6178 6973 2e20 out the y-axis. \n-00015b20: 2057 6865 6e20 6170 706c 6965 6420 746f When applied to\n-00015b30: 20e2 8098 2870 3129 202d 2028 4f29 e280 ...(p1) - (O)..\n-00015b40: 992c 2074 6865 0a72 6573 756c 7469 6e67 ., the.resulting\n-00015b50: 2076 6563 746f 7220 706f 696e 7473 2074 vector points t\n-00015b60: 6f20 7468 6520 7269 6768 7420 6173 2073 o the right as s\n-00015b70: 686f 776e 2e20 2049 6e20 7468 6973 206d hown. In this m\n-00015b80: 616e 6e65 722c 2077 6520 6361 6e0a 7069 anner, we can.pi\n-00015b90: 636b 2061 6e79 2076 6572 7465 7820 6173 ck any vertex as\n-00015ba0: 2074 6865 206c 6f63 6174 696f 6e20 6f66 the location of\n-00015bb0: 2074 6865 2068 6569 6768 7420 6469 6d65 the height dime\n-00015bc0: 6e73 696f 6e20 6c69 6e65 7320 6279 2076 nsion lines by v\n-00015bd0: 6172 7969 6e67 0a74 6865 2065 7870 6f6e arying.the expon\n-00015be0: 656e 7420 6f66 20e2 8098 5b5b 7365 675f ent of ...[[seg_\n-00015bf0: 726f 745d 5de2 8099 2e20 2054 6869 7320 rot]].... This \n-00015c00: 6973 206f 6e6c 7920 6f6e 6520 6f66 206d is only one of m\n-00015c10: 616e 7920 706f 7373 6962 6c65 0a73 7472 any possible.str\n-00015c20: 6174 6567 6965 732e 0a0a 2020 2054 6865 ategies... The\n-00015c30: 2063 6f6d 7075 7461 7469 6f6e 206f 6620 computation of \n-00015c40: e280 9868 6d32 e280 9920 6973 2061 2075 ...hm2... is a u\n-00015c50: 7365 6675 6c20 6964 696f 6d20 666f 7220 seful idiom for \n-00015c60: 6669 6e64 696e 6720 7468 6520 6365 6e74 finding the cent\n-00015c70: 726f 6964 0a6f 6620 6120 7365 7420 6f66 roid.of a set of\n-00015c80: 2070 6f69 6e74 732e 0a0a 2020 2054 6865 points... The\n-00015c90: 2074 776f 2072 6164 6975 7320 6d61 726b two radius mark\n-00015ca0: 7320 6172 6520 646f 6e65 2073 696d 696c s are done simil\n-00015cb0: 6172 6c79 2c20 736f 2077 6520 7072 6573 arly, so we pres\n-00015cc0: 656e 7420 7468 6520 636f 6465 0a77 6974 ent the code.wit\n-00015cd0: 686f 7574 2063 6f6d 6d65 6e74 2e0a 2020 hout comment.. \n-00015ce0: 2520 7261 6469 7573 206d 6561 7375 7265 % radius measure\n-00015cf0: 6d65 6e74 206d 6172 6b73 0a20 2064 6566 ment marks. def\n-00015d00: 2067 6170 205b 302c 2e32 2c30 5d20 2025 gap [0,.2,0] %\n-00015d10: 2075 7365 6420 746f 2063 7265 6174 6520 used to create \n-00015d20: 736d 616c 6c20 7665 7274 6963 616c 2067 small vertical g\n-00015d30: 6170 730a 0a20 2025 2066 6972 7374 2072 aps.. % first r\n-00015d40: 310a 2020 6465 6620 7570 3120 5b30 2c33 1. def up1 [0,3\n-00015d50: 2e31 2c30 5d20 2520 7469 636b 2072 6973 .1,0] % tick ris\n-00015d60: 6573 2061 626f 7665 2064 696d 656e 7369 es above dimensi\n-00015d70: 6f6e 2061 206c 6974 746c 650a 2020 6465 on a little. de\n-00015d80: 6620 7231 2028 2870 3129 2074 6865 6e20 f r1 ((p1) then \n-00015d90: 5b5b 7365 675f 726f 745d 5d5e 2d32 2920 [[seg_rot]]^-2) \n-00015da0: 2b20 5b75 7031 5d0a 2020 6465 6620 7231 + [up1]. def r1\n-00015db0: 6320 2872 3129 2074 6865 6e20 7363 616c c (r1) then scal\n-00015dc0: 6528 5b4a 5d29 0a20 2064 6566 2072 3174 e([J]). def r1t\n-00015dd0: 2028 7231 2920 2b20 5b67 6170 5d0a 2020 (r1) + [gap]. \n-00015de0: 6465 6620 7231 6220 2828 7231 7429 2074 def r1b ((r1t) t\n-00015df0: 6865 6e20 7363 616c 6528 5b31 2c30 2c31 hen scale([1,0,1\n-00015e00: 5d29 2920 2b20 5b67 6170 5d0a 2020 6c69 ])) + [gap]. li\n-00015e10: 6e65 5b61 7272 6f77 733d 3c2d 3e5d 2872 ne[arrows=<->](r\n-00015e20: 3163 2928 7231 2920 2025 2064 696d 656e 1c)(r1) % dimen\n-00015e30: 7369 6f6e 206c 696e 650a 2020 6c69 6e65 sion line. line\n-00015e40: 2872 3162 2928 7231 7429 2020 2020 2020 (r1b)(r1t) \n-00015e50: 2020 2020 2020 2025 2074 6963 6b0a 2020 % tick. \n-00015e60: 6465 6620 7231 6d20 2828 7231 2920 2d20 def r1m ((r1) - \n-00015e70: 284f 2920 2b20 2872 3163 2920 2d20 284f (O) + (r1c) - (O\n-00015e80: 2929 202f 2032 202b 2028 4f29 2025 206c )) / 2 + (O) % l\n-00015e90: 6162 656c 2070 6f73 6974 696f 6e0a 2020 abel position. \n-00015ea0: 7370 6563 6961 6c20 7c5c 666f 6f74 6e6f special |\\footno\n-00015eb0: 7465 7369 7a65 5c72 7075 742a 2331 7b24 tesize\\rput*#1{$\n-00015ec0: 725f 3124 7d7c 2872 316d 2920 2025 206c r_1$}|(r1m) % l\n-00015ed0: 6162 656c 0a0a 2020 2520 7361 6d65 2064 abel.. % same d\n-00015ee0: 7269 6c6c 2066 6f72 2072 302c 2062 7574 rill for r0, but\n-00015ef0: 206d 7573 7420 7072 6f6a 6563 7420 646f must project do\n-00015f00: 776e 2066 6972 7374 0a20 2064 6566 2075 wn first. def u\n-00015f10: 7030 205b 302c 322e 372c 305d 0a20 2064 p0 [0,2.7,0]. d\n-00015f20: 6566 2072 3020 2828 7030 2920 7468 656e ef r0 ((p0) then\n-00015f30: 2073 6361 6c65 285b 312c 302c 315d 2920 scale([1,0,1]) \n-00015f40: 7468 656e 205b 5b73 6567 5f72 6f74 5d5d then [[seg_rot]]\n-00015f50: 5e2d 3229 202b 205b 7570 305d 0a20 2064 ^-2) + [up0]. d\n-00015f60: 6566 2072 3063 2028 7230 2920 7468 656e ef r0c (r0) then\n-00015f70: 2073 6361 6c65 285b 4a5d 290a 2020 6465 scale([J]). de\n-00015f80: 6620 7230 7420 2872 3029 202b 205b 6761 f r0t (r0) + [ga\n-00015f90: 705d 0a20 2064 6566 2072 3062 2028 2870 p]. def r0b ((p\n-00015fa0: 3029 2074 6865 6e20 5b5b 7365 675f 726f 0) then [[seg_ro\n-00015fb0: 745d 5d5e 2d32 2920 2b20 5b67 6170 5d0a t]]^-2) + [gap].\n-00015fc0: 2020 6c69 6e65 5b61 7272 6f77 733d 3c2d line[arrows=<-\n-00015fd0: 3e5d 2872 3063 2928 7230 290a 2020 6c69 >](r0c)(r0). li\n-00015fe0: 6e65 2872 3062 2928 7230 7429 0a20 2064 ne(r0b)(r0t). d\n-00015ff0: 6566 2072 306d 2028 2872 3029 202d 2028 ef r0m ((r0) - (\n-00016000: 4f29 202b 2028 7230 6329 202d 2028 4f29 O) + (r0c) - (O)\n-00016010: 2920 2f20 3220 2b20 284f 290a 2020 7370 ) / 2 + (O). sp\n-00016020: 6563 6961 6c20 7c5c 666f 6f74 6e6f 7465 ecial |\\footnote\n-00016030: 7369 7a65 5c72 7075 742a 2331 7b24 725f size\\rput*#1{$r_\n-00016040: 3024 7d7c 2872 306d 290a 0a20 2020 5468 0$}|(r0m).. Th\n-00016050: 6520 7365 636f 6e64 2064 7261 7769 6e67 e second drawing\n-00016060: 2075 7365 7320 7468 6520 7361 6d65 2074 uses the same t\n-00016070: 6563 686e 6971 7565 732e 2020 4f6e 6c79 echniques. Only\n-00016080: 2074 6865 206d 6574 686f 6420 666f 720a the method for.\n-00016090: 6472 6177 696e 6720 7468 6520 656c 6c69 drawing the elli\n-000160a0: 7074 6963 616c 2061 7263 2069 7320 6e65 ptical arc is ne\n-000160b0: 772e 2020 4865 7265 2069 7320 7468 6520 w. Here is the \n-000160c0: 636f 6465 2e0a 2020 6465 6620 6d69 6420 code.. def mid \n-000160d0: 2828 7030 3029 2d28 4f29 2b28 7031 3029 ((p00)-(O)+(p10)\n-000160e0: 2d28 4f29 2b28 7031 3129 2d28 4f29 2b28 -(O)+(p11)-(O)+(\n-000160f0: 7030 3129 2d28 4f29 292f 342b 284f 290a p01)-(O))/4+(O).\n-00016100: 2020 7370 6563 6961 6c7c 5c72 7075 7423 special|\\rput#\n-00016110: 317b 5c70 7363 7573 746f 6d7b 0a20 2020 1{\\pscustom{. \n-00016120: 205c 7363 616c 657b 3120 312e 337d 0a20 \\scale{1 1.3}. \n-00016130: 2020 205c 7073 6172 635b 6172 726f 776c \\psarc[arrowl\n-00016140: 656e 6774 683d 2e35 5d7b 2d3e 7d7b 2e32 ength=.5]{->}{.2\n-00016150: 357d 7b2d 3630 7d7b 3234 307d 7d7d 7c0a 5}{-60}{240}}}|.\n-00016160: 2020 2020 5b6c 6179 3d6f 7665 725d 286d [lay=over](m\n-00016170: 6964 290a 5765 2063 6f75 6c64 2068 6176 id).We could hav\n-00016180: 6520 7377 6570 7420 6120 706f 696e 7420 e swept a point \n-00016190: 746f 206d 616b 6520 7468 6520 6172 6320 to make the arc \n-000161a0: 7769 7468 20e2 8098 736b 6574 6368 e280 with ...sketch..\n-000161b0: 992c 2062 7574 2075 7369 6e67 2061 0ae2 ., but using a..\n-000161c0: 8098 5053 5472 6963 6b73 e280 9920 6375 ..PSTricks... cu\n-000161d0: 7374 6f6d 2067 7261 7068 6963 2077 6173 stom graphic was\n-000161e0: 2073 696d 706c 6572 2e20 2041 6761 696e simpler. Again\n-000161f0: 2077 6520 636f 6d70 7574 6564 2074 6865 we computed the\n-00016200: 2063 656e 7472 6f69 640a 6f66 2074 6865 centroid.of the\n-00016210: 2071 7561 6472 696c 6174 6572 616c 2062 quadrilateral b\n-00016220: 7920 6176 6572 6167 696e 6720 706f 696e y averaging poin\n-00016230: 7473 2e20 204e 6f74 6520 7468 6174 2073 ts. Note that s\n-00016240: 6361 6c69 6e67 2069 6e0a 506f 7374 7363 caling in.Postsc\n-00016250: 7269 7074 2064 6973 746f 7274 7320 7468 ript distorts th\n-00016260: 6520 6172 726f 7768 6561 642c 2062 7574 e arrowhead, but\n-00016270: 2069 6e20 7468 6973 2063 6173 6520 7468 in this case th\n-00016280: 6520 6469 7374 6f72 7469 6f6e 0a61 6374 e distortion.act\n-00016290: 7561 6c6c 7920 6c6f 6f6b 7320 6265 7474 ually looks bett\n-000162a0: 6572 2069 6e20 7468 6520 7072 6f6a 6563 er in the projec\n-000162b0: 7469 6f6e 206f 6620 7468 6520 736c 616e tion of the slan\n-000162c0: 7465 6420 6661 6365 2e20 2041 20e2 8098 ted face. A ...\n-000162d0: 736b 6574 6368 e280 990a 6172 726f 7768 sketch....arrowh\n-000162e0: 6561 6420 776f 756c 6420 6e6f 7420 6861 ead would not ha\n-000162f0: 7665 2062 6565 6e20 6469 7374 6f72 7465 ve been distorte\n-00016300: 642e 0a0a 2020 2054 6865 2063 6f6d 706c d... The compl\n-00016310: 6574 6520 636f 6465 2066 6f72 2074 6869 ete code for thi\n-00016320: 7320 6578 616d 706c 652c 2077 6869 6368 s example, which\n-00016330: 2064 7261 7773 2065 6974 6865 7220 6669 draws either fi\n-00016340: 6775 7265 0a64 6570 656e 6469 6e67 206f gure.depending o\n-00016350: 6e20 7468 6520 6465 6669 6e69 7469 6f6e n the definition\n-00016360: 206f 6620 7468 6520 7461 6720 e280 983c of the tag ...<\n-00016370: 6c61 6265 6c65 643e e280 992c 2069 7320 labeled>..., is \n-00016380: 696e 636c 7564 6564 2069 6e20 7468 650a included in the.\n-00016390: e280 9873 6b65 7463 68e2 8099 2064 6973 ...sketch... dis\n-000163a0: 7472 6962 7574 696f 6e20 696e 2074 6865 tribution in the\n-000163b0: 2066 696c 6520 e280 9874 7275 6e63 6174 file ...truncat\n-000163c0: 6564 636f 6e65 2e73 6be2 8099 2e0a 0a1f edcone.sk.......\n-000163d0: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-000163e0: 666f 2c20 204e 6f64 653a 2041 2068 6965 fo, Node: A hie\n-000163f0: 7261 7263 6869 6361 6c20 6d6f 6465 6c2c rarchical model,\n-00016400: 2020 4e65 7874 3a20 4361 7665 6174 732c Next: Caveats,\n-00016410: 2020 5072 6576 3a20 4120 7465 6368 6e69 Prev: A techni\n-00016420: 6361 6c20 6472 6177 696e 672c 2020 5570 cal drawing, Up\n-00016430: 3a20 4275 696c 6469 6e67 2061 2064 7261 : Building a dra\n-00016440: 7769 6e67 0a0a 342e 3320 4120 6869 6572 wing..4.3 A hier\n-00016450: 6172 6368 6963 616c 206d 6f64 656c 0a3d archical model.=\n+000151a0: 3d3d 3d3d 3d0a 0a4c 6574 2773 206c 6f6f =====..Let's loo\n+000151b0: 6b20 6174 2061 2064 7261 7769 6e67 2074 k at a drawing t\n+000151c0: 6861 7420 7265 7072 6573 656e 7473 2074 hat represents t\n+000151d0: 6865 206b 696e 6420 6f66 2070 726f 626c he kind of probl\n+000151e0: 656d 20e2 8098 736b 6574 6368 e280 9920 em ...sketch... \n+000151f0: 7761 730a 6d65 616e 7420 746f 2073 6f6c was.meant to sol\n+00015200: 7665 2d2d 6120 7061 6972 206f 6620 7465 ve--a pair of te\n+00015210: 7874 626f 6f6b 2066 6967 7572 6573 2072 xtbook figures r\n+00015220: 6567 6172 6469 6e67 2061 2070 6f6c 7967 egarding a polyg\n+00015230: 6f6e 616c 0a61 7070 726f 7869 6d61 7469 onal.approximati\n+00015240: 6f6e 206f 6620 6120 7472 756e 6361 7465 on of a truncate\n+00015250: 6420 636f 6e65 2e20 2048 6572 6520 6172 d cone. Here ar\n+00015260: 6520 7468 6520 7069 6374 7572 6573 2077 e the pictures w\n+00015270: 6520 7769 6c6c 0a70 726f 6475 6365 2e0a e will.produce..\n+00015280: 0a00 085b 696d 6167 6520 7372 633d 2265 ...[image src=\"e\n+00015290: 7832 3530 2e70 6e67 2220 7465 7874 3d22 x250.png\" text=\"\n+000152a0: 496d 6167 6520 6578 3235 3020 6f6d 6974 Image ex250 omit\n+000152b0: 7465 6420 696e 2074 6578 7420 7665 7273 ted in text vers\n+000152c0: 696f 6e20 6f66 2074 6869 7320 646f 6375 ion of this docu\n+000152d0: 6d65 6e74 2e22 0008 5d20 2020 2020 0008 ment.\"..] ..\n+000152e0: 5b69 6d61 6765 2073 7263 3d22 6578 3236 [image src=\"ex26\n+000152f0: 302e 706e 6722 2074 6578 743d 2249 6d61 0.png\" text=\"Ima\n+00015300: 6765 2065 7832 3630 206f 6d69 7474 6564 ge ex260 omitted\n+00015310: 2069 6e20 7465 7874 2076 6572 7369 6f6e in text version\n+00015320: 206f 6620 7468 6973 2064 6f63 756d 656e of this documen\n+00015330: 742e 2200 085d 0a0a 2020 2054 6865 2063 t.\"..].. The c\n+00015340: 6f6e 6520 7368 6170 6520 6973 206a 7573 one shape is jus\n+00015350: 7420 6120 7377 6570 7420 6c69 6e65 2077 t a swept line w\n+00015360: 6974 6820 6e6f 2063 6c6f 7375 7265 2074 ith no closure t\n+00015370: 6167 2061 6e64 2063 756c 6c69 6e67 0a74 ag and culling.t\n+00015380: 7572 6e65 6420 6f66 662e 2020 4265 6769 urned off. Begi\n+00015390: 6e20 6279 2073 6574 7469 6e67 2075 7020 n by setting up \n+000153a0: 736f 6d65 2075 7365 6675 6c20 636f 6e73 some useful cons\n+000153b0: 7461 6e74 732e 0a20 2064 6566 204f 2028 tants.. def O (\n+000153c0: 302c 302c 3029 2064 6566 2049 205b 312c 0,0,0) def I [1,\n+000153d0: 302c 305d 2064 6566 204a 205b 302c 312c 0,0] def J [0,1,\n+000153e0: 305d 2064 6566 204b 205b 302c 302c 315d 0] def K [0,0,1]\n+000153f0: 0a20 2064 6566 2070 3020 2831 2c32 2920 . def p0 (1,2) \n+00015400: 6465 6620 7031 2028 312e 352c 3029 2064 def p1 (1.5,0) d\n+00015410: 6566 204e 2038 0a20 2064 6566 2073 6567 ef N 8. def seg\n+00015420: 5f72 6f74 2072 6f74 6174 6528 3336 3020 _rot rotate(360 \n+00015430: 2f20 4e2c 205b 4a5d 290a 5468 6520 706f / N, [J]).The po\n+00015440: 696e 7473 20e2 8098 7030 e280 9920 616e ints ...p0... an\n+00015450: 6420 e280 9870 31e2 8099 2061 7265 2074 d ...p1... are t\n+00015460: 6865 2065 6e64 2070 6f69 6e74 7320 6f66 he end points of\n+00015470: 2074 6865 206c 696e 6520 746f 2062 6520 the line to be \n+00015480: 7377 6570 742e 0a54 6865 2064 6566 696e swept..The defin\n+00015490: 6974 696f 6e20 e280 9873 6567 5f72 6f74 ition ...seg_rot\n+000154a0: e280 9920 6973 2074 6865 2073 7765 6570 ... is the sweep\n+000154b0: 2074 7261 6e73 666f 726d 6174 696f 6e2e transformation.\n+000154c0: 2020 5769 7468 2074 6865 7365 2c20 7468 With these, th\n+000154d0: 650a 636f 6e65 2069 7473 656c 6620 6973 e.cone itself is\n+000154e0: 2073 696d 706c 652e 0a20 2073 7765 6570 simple.. sweep\n+000154f0: 5b63 756c 6c3d 6661 6c73 655d 207b 204e [cull=false] { N\n+00015500: 2c20 5b5b 7365 675f 726f 745d 5d20 7d20 , [[seg_rot]] } \n+00015510: 6c69 6e65 2870 3029 2870 3129 0a0a 2020 line(p0)(p1).. \n+00015520: 2054 6865 2061 7865 7320 6172 6520 6e65 The axes are ne\n+00015530: 7874 2061 6e64 2069 6e63 6c75 6465 2061 xt and include a\n+00015540: 6e20 696e 7465 7265 7369 6e67 2074 7269 n interesing tri\n+00015550: 636b 2074 6861 7420 7368 6f77 7320 7468 ck that shows th\n+00015560: 650a 6869 6464 656e 2070 6172 7473 2061 e.hidden parts a\n+00015570: 7320 646f 7474 6564 206c 696e 6573 2e20 s dotted lines. \n+00015580: 2054 6865 2073 6563 7265 7420 6973 2064 The secret is d\n+00015590: 7261 7720 7468 6520 6178 6573 2074 7769 raw the axes twi\n+000155a0: 6365 2d2d 736f 6c69 640a 6c69 6e65 7320 ce--solid.lines \n+000155b0: 7769 7468 2074 6865 206e 6f72 6d61 6c20 with the normal \n+000155c0: 6869 6464 656e 2073 7572 6661 6365 2061 hidden surface a\n+000155d0: 6c67 6f72 6974 686d 2069 6e20 6566 6665 lgorithm in effe\n+000155e0: 6374 2c20 616e 6420 7468 656e 0a64 6f74 ct, and then.dot\n+000155f0: 7465 6420 7769 7468 2074 6865 206f 7074 ted with the opt\n+00015600: 696f 6e20 e280 986c 6179 3d6f 7665 72e2 ion ...lay=over.\n+00015610: 8099 2073 6f20 7468 6174 206e 6f20 706f .. so that no po\n+00015620: 6c79 676f 6e73 2063 616e 2068 6964 6520 lygons can hide \n+00015630: 7468 656d 2e0a 2020 6465 6620 6178 2028 them.. def ax (\n+00015640: 6478 2c30 2c30 2920 2520 7469 7073 206f dx,0,0) % tips o\n+00015650: 6620 7468 6520 6178 6573 0a20 2064 6566 f the axes. def\n+00015660: 2061 7920 2830 2c64 792c 3029 0a20 2064 ay (0,dy,0). d\n+00015670: 6566 2061 7a20 2830 2c30 2c64 7a29 0a20 ef az (0,0,dz). \n+00015680: 206c 696e 655b 6172 726f 7773 3d3c 2d3e line[arrows=<->\n+00015690: 2c6c 696e 6577 6964 7468 3d2e 3470 745d ,linewidth=.4pt]\n+000156a0: 2861 7829 284f 2928 6179 290a 2020 6c69 (ax)(O)(ay). li\n+000156b0: 6e65 5b61 7272 6f77 733d 2d3e 2c6c 696e ne[arrows=->,lin\n+000156c0: 6577 6964 7468 3d2e 3470 745d 284f 2928 ewidth=.4pt](O)(\n+000156d0: 617a 290a 2020 2520 7265 7065 6174 2064 az). % repeat d\n+000156e0: 6f74 7465 6420 6173 2061 6e20 6f76 6572 otted as an over\n+000156f0: 6c61 7920 746f 2068 696e 7420 6174 2074 lay to hint at t\n+00015700: 6865 2068 6964 6465 6e20 6c69 6e65 730a he hidden lines.\n+00015710: 2020 6c69 6e65 5b6c 6179 3d6f 7665 722c line[lay=over,\n+00015720: 6c69 6e65 7374 796c 653d 646f 7474 6564 linestyle=dotted\n+00015730: 2c6c 696e 6577 6964 7468 3d2e 3470 745d ,linewidth=.4pt]\n+00015740: 2861 7829 284f 2928 6179 290a 2020 6c69 (ax)(O)(ay). li\n+00015750: 6e65 5b6c 6179 3d6f 7665 722c 6c69 6e65 ne[lay=over,line\n+00015760: 7374 796c 653d 646f 7474 6564 2c6c 696e style=dotted,lin\n+00015770: 6577 6964 7468 3d2e 3470 745d 284f 2928 ewidth=.4pt](O)(\n+00015780: 617a 290a 2020 7370 6563 6961 6c7c 5c66 az). special|\\f\n+00015790: 6f6f 746e 6f74 6573 697a 650a 2020 2020 ootnotesize. \n+000157a0: 2020 2020 2020 5c75 7075 745b 645d 2331 \\uput[d]#1\n+000157b0: 7b24 7824 7d5c 7570 7574 5b75 5d23 327b {$x$}\\uput[u]#2{\n+000157c0: 2479 247d 5c75 7075 745b 6c5d 2333 7b24 $y$}\\uput[l]#3{$\n+000157d0: 7a24 7d7c 0a20 2020 2028 6178 2928 6179 z$}|. (ax)(ay\n+000157e0: 2928 617a 290a 5468 6520 6c61 6265 6c73 )(az).The labels\n+000157f0: 2061 7265 2061 7070 6c69 6564 2077 6974 are applied wit\n+00015800: 6820 e280 9850 5354 7269 636b 73e2 8099 h ...PSTricks...\n+00015810: 2073 7065 6369 616c 206f 626a 6563 7473 special objects\n+00015820: 2061 7320 7573 7561 6c2e 0a0a 2020 2046 as usual... F\n+00015830: 6f72 2074 6865 2068 6569 6768 7420 6469 or the height di\n+00015840: 6d65 6e73 696f 6e20 6d61 726b 2c20 7468 mension mark, th\n+00015850: 6520 706f 7765 7220 6f66 2061 6666 696e e power of affin\n+00015860: 6520 6172 6974 6865 7469 6320 6973 2076 e arithetic is v\n+00015870: 6572 790a 6865 6c70 6675 6c2e 0a20 2064 ery.helpful.. d\n+00015880: 6566 2068 6469 6d5f 7265 6620 756e 6974 ef hdim_ref unit\n+00015890: 2828 7031 2920 2d20 284f 2929 2074 6865 ((p1) - (O)) the\n+000158a0: 6e20 5b5b 7365 675f 726f 745d 5d5e 320a n [[seg_rot]]^2.\n+000158b0: 2020 6465 6620 6330 2028 7030 2920 7468 def c0 (p0) th\n+000158c0: 656e 2073 6361 6c65 285b 4a5d 290a 2020 en scale([J]). \n+000158d0: 6465 6620 6830 3020 2863 3029 202b 2031 def h00 (c0) + 1\n+000158e0: 2e31 202a 205b 6864 696d 5f72 6566 5d0a .1 * [hdim_ref].\n+000158f0: 2020 6465 6620 6830 3120 2863 3029 202b def h01 (c0) +\n+00015900: 2031 2e39 202a 205b 6864 696d 5f72 6566 1.9 * [hdim_ref\n+00015910: 5d0a 2020 6465 6620 6830 3220 2863 3029 ]. def h02 (c0)\n+00015920: 202b 2031 2e38 202a 205b 6864 696d 5f72 + 1.8 * [hdim_r\n+00015930: 6566 5d0a 2020 6c69 6e65 2868 3030 2928 ef]. line(h00)(\n+00015940: 6830 3129 0a20 2064 6566 2068 3130 2028 h01). def h10 (\n+00015950: 4f29 202b 2031 2e36 202a 205b 6864 696d O) + 1.6 * [hdim\n+00015960: 5f72 6566 5d0a 2020 6465 6620 6831 3120 _ref]. def h11 \n+00015970: 284f 2920 2b20 312e 3920 2a20 5b68 6469 (O) + 1.9 * [hdi\n+00015980: 6d5f 7265 665d 0a20 2064 6566 2068 3132 m_ref]. def h12\n+00015990: 2028 4f29 202b 2031 2e38 202a 205b 6864 (O) + 1.8 * [hd\n+000159a0: 696d 5f72 6566 5d0a 2020 6c69 6e65 2868 im_ref]. line(h\n+000159b0: 3130 2928 6831 3129 0a20 206c 696e 655b 10)(h11). line[\n+000159c0: 6172 726f 7773 3d3c 2d3e 5d28 6830 3229 arrows=<->](h02)\n+000159d0: 2868 3132 290a 2020 6465 6620 686d 3220 (h12). def hm2 \n+000159e0: 2828 6830 3229 202d 2028 4f29 202b 2028 ((h02) - (O) + (\n+000159f0: 6831 3229 202d 2028 4f29 2920 2f20 3220 h12) - (O)) / 2 \n+00015a00: 2b20 284f 290a 2020 7370 6563 6961 6c7c + (O). special|\n+00015a10: 5c66 6f6f 746e 6f74 6573 697a 655c 7270 \\footnotesize\\rp\n+00015a20: 7574 2a23 317b 2468 247d 7c28 686d 3229 ut*#1{$h$}|(hm2)\n+00015a30: 0a20 2020 5468 6520 6765 6e65 7261 6c20 . The general \n+00015a40: 6964 6561 2065 6d70 6c6f 7965 6420 6865 idea employed he\n+00015a50: 7265 2069 7320 746f 2063 6f6d 7075 7465 re is to compute\n+00015a60: 2061 2075 6e69 7420 2272 6566 6572 656e a unit \"referen\n+00015a70: 6365 0a76 6563 746f 7222 2070 6172 616c ce.vector\" paral\n+00015a80: 6c65 6c20 746f 2074 6865 2078 7a2d 706c lel to the xz-pl\n+00015a90: 616e 6520 696e 2074 6865 2064 6573 6972 ane in the desir\n+00015aa0: 6564 2064 6972 6563 7469 6f6e 206f 6620 ed direction of \n+00015ab0: 7468 650a 6469 6d65 6e73 696f 6e20 6672 the.dimension fr\n+00015ac0: 6f6d 2074 6865 206f 7269 6769 6e2e 2020 om the origin. \n+00015ad0: 5468 6520 7472 616e 7366 6f72 6d61 7469 The transformati\n+00015ae0: 6f6e 20e2 8098 5b5b 7365 675f 726f 745d on ...[[seg_rot]\n+00015af0: 5d5e 32e2 8099 2072 6f74 6174 6573 0a74 ]^2... rotates.t\n+00015b00: 776f 2073 6567 6d65 6e74 7320 6162 6f75 wo segments abou\n+00015b10: 7420 7468 6520 792d 6178 6973 2e20 2057 t the y-axis. W\n+00015b20: 6865 6e20 6170 706c 6965 6420 746f 20e2 hen applied to .\n+00015b30: 8098 2870 3129 202d 2028 4f29 e280 992c ..(p1) - (O)...,\n+00015b40: 2074 6865 0a72 6573 756c 7469 6e67 2076 the.resulting v\n+00015b50: 6563 746f 7220 706f 696e 7473 2074 6f20 ector points to \n+00015b60: 7468 6520 7269 6768 7420 6173 2073 686f the right as sho\n+00015b70: 776e 2e20 2049 6e20 7468 6973 206d 616e wn. In this man\n+00015b80: 6e65 722c 2077 6520 6361 6e0a 7069 636b ner, we can.pick\n+00015b90: 2061 6e79 2076 6572 7465 7820 6173 2074 any vertex as t\n+00015ba0: 6865 206c 6f63 6174 696f 6e20 6f66 2074 he location of t\n+00015bb0: 6865 2068 6569 6768 7420 6469 6d65 6e73 he height dimens\n+00015bc0: 696f 6e20 6c69 6e65 7320 6279 2076 6172 ion lines by var\n+00015bd0: 7969 6e67 0a74 6865 2065 7870 6f6e 656e ying.the exponen\n+00015be0: 7420 6f66 20e2 8098 5b5b 7365 675f 726f t of ...[[seg_ro\n+00015bf0: 745d 5de2 8099 2e20 2054 6869 7320 6973 t]].... This is\n+00015c00: 206f 6e6c 7920 6f6e 6520 6f66 206d 616e only one of man\n+00015c10: 7920 706f 7373 6962 6c65 0a73 7472 6174 y possible.strat\n+00015c20: 6567 6965 732e 0a0a 2020 2054 6865 2063 egies... The c\n+00015c30: 6f6d 7075 7461 7469 6f6e 206f 6620 e280 omputation of ..\n+00015c40: 9868 6d32 e280 9920 6973 2061 2075 7365 .hm2... is a use\n+00015c50: 6675 6c20 6964 696f 6d20 666f 7220 6669 ful idiom for fi\n+00015c60: 6e64 696e 6720 7468 6520 6365 6e74 726f nding the centro\n+00015c70: 6964 0a6f 6620 6120 7365 7420 6f66 2070 id.of a set of p\n+00015c80: 6f69 6e74 732e 0a0a 2020 2054 6865 2074 oints... The t\n+00015c90: 776f 2072 6164 6975 7320 6d61 726b 7320 wo radius marks \n+00015ca0: 6172 6520 646f 6e65 2073 696d 696c 6172 are done similar\n+00015cb0: 6c79 2c20 736f 2077 6520 7072 6573 656e ly, so we presen\n+00015cc0: 7420 7468 6520 636f 6465 0a77 6974 686f t the code.witho\n+00015cd0: 7574 2063 6f6d 6d65 6e74 2e0a 2020 2520 ut comment.. % \n+00015ce0: 7261 6469 7573 206d 6561 7375 7265 6d65 radius measureme\n+00015cf0: 6e74 206d 6172 6b73 0a20 2064 6566 2067 nt marks. def g\n+00015d00: 6170 205b 302c 2e32 2c30 5d20 2025 2075 ap [0,.2,0] % u\n+00015d10: 7365 6420 746f 2063 7265 6174 6520 736d sed to create sm\n+00015d20: 616c 6c20 7665 7274 6963 616c 2067 6170 all vertical gap\n+00015d30: 730a 0a20 2025 2066 6972 7374 2072 310a s.. % first r1.\n+00015d40: 2020 6465 6620 7570 3120 5b30 2c33 2e31 def up1 [0,3.1\n+00015d50: 2c30 5d20 2520 7469 636b 2072 6973 6573 ,0] % tick rises\n+00015d60: 2061 626f 7665 2064 696d 656e 7369 6f6e above dimension\n+00015d70: 2061 206c 6974 746c 650a 2020 6465 6620 a little. def \n+00015d80: 7231 2028 2870 3129 2074 6865 6e20 5b5b r1 ((p1) then [[\n+00015d90: 7365 675f 726f 745d 5d5e 2d32 2920 2b20 seg_rot]]^-2) + \n+00015da0: 5b75 7031 5d0a 2020 6465 6620 7231 6320 [up1]. def r1c \n+00015db0: 2872 3129 2074 6865 6e20 7363 616c 6528 (r1) then scale(\n+00015dc0: 5b4a 5d29 0a20 2064 6566 2072 3174 2028 [J]). def r1t (\n+00015dd0: 7231 2920 2b20 5b67 6170 5d0a 2020 6465 r1) + [gap]. de\n+00015de0: 6620 7231 6220 2828 7231 7429 2074 6865 f r1b ((r1t) the\n+00015df0: 6e20 7363 616c 6528 5b31 2c30 2c31 5d29 n scale([1,0,1])\n+00015e00: 2920 2b20 5b67 6170 5d0a 2020 6c69 6e65 ) + [gap]. line\n+00015e10: 5b61 7272 6f77 733d 3c2d 3e5d 2872 3163 [arrows=<->](r1c\n+00015e20: 2928 7231 2920 2025 2064 696d 656e 7369 )(r1) % dimensi\n+00015e30: 6f6e 206c 696e 650a 2020 6c69 6e65 2872 on line. line(r\n+00015e40: 3162 2928 7231 7429 2020 2020 2020 2020 1b)(r1t) \n+00015e50: 2020 2020 2025 2074 6963 6b0a 2020 6465 % tick. de\n+00015e60: 6620 7231 6d20 2828 7231 2920 2d20 284f f r1m ((r1) - (O\n+00015e70: 2920 2b20 2872 3163 2920 2d20 284f 2929 ) + (r1c) - (O))\n+00015e80: 202f 2032 202b 2028 4f29 2025 206c 6162 / 2 + (O) % lab\n+00015e90: 656c 2070 6f73 6974 696f 6e0a 2020 7370 el position. sp\n+00015ea0: 6563 6961 6c20 7c5c 666f 6f74 6e6f 7465 ecial |\\footnote\n+00015eb0: 7369 7a65 5c72 7075 742a 2331 7b24 725f size\\rput*#1{$r_\n+00015ec0: 3124 7d7c 2872 316d 2920 2025 206c 6162 1$}|(r1m) % lab\n+00015ed0: 656c 0a0a 2020 2520 7361 6d65 2064 7269 el.. % same dri\n+00015ee0: 6c6c 2066 6f72 2072 302c 2062 7574 206d ll for r0, but m\n+00015ef0: 7573 7420 7072 6f6a 6563 7420 646f 776e ust project down\n+00015f00: 2066 6972 7374 0a20 2064 6566 2075 7030 first. def up0\n+00015f10: 205b 302c 322e 372c 305d 0a20 2064 6566 [0,2.7,0]. def\n+00015f20: 2072 3020 2828 7030 2920 7468 656e 2073 r0 ((p0) then s\n+00015f30: 6361 6c65 285b 312c 302c 315d 2920 7468 cale([1,0,1]) th\n+00015f40: 656e 205b 5b73 6567 5f72 6f74 5d5d 5e2d en [[seg_rot]]^-\n+00015f50: 3229 202b 205b 7570 305d 0a20 2064 6566 2) + [up0]. def\n+00015f60: 2072 3063 2028 7230 2920 7468 656e 2073 r0c (r0) then s\n+00015f70: 6361 6c65 285b 4a5d 290a 2020 6465 6620 cale([J]). def \n+00015f80: 7230 7420 2872 3029 202b 205b 6761 705d r0t (r0) + [gap]\n+00015f90: 0a20 2064 6566 2072 3062 2028 2870 3029 . def r0b ((p0)\n+00015fa0: 2074 6865 6e20 5b5b 7365 675f 726f 745d then [[seg_rot]\n+00015fb0: 5d5e 2d32 2920 2b20 5b67 6170 5d0a 2020 ]^-2) + [gap]. \n+00015fc0: 6c69 6e65 5b61 7272 6f77 733d 3c2d 3e5d line[arrows=<->]\n+00015fd0: 2872 3063 2928 7230 290a 2020 6c69 6e65 (r0c)(r0). line\n+00015fe0: 2872 3062 2928 7230 7429 0a20 2064 6566 (r0b)(r0t). def\n+00015ff0: 2072 306d 2028 2872 3029 202d 2028 4f29 r0m ((r0) - (O)\n+00016000: 202b 2028 7230 6329 202d 2028 4f29 2920 + (r0c) - (O)) \n+00016010: 2f20 3220 2b20 284f 290a 2020 7370 6563 / 2 + (O). spec\n+00016020: 6961 6c20 7c5c 666f 6f74 6e6f 7465 7369 ial |\\footnotesi\n+00016030: 7a65 5c72 7075 742a 2331 7b24 725f 3024 ze\\rput*#1{$r_0$\n+00016040: 7d7c 2872 306d 290a 0a20 2020 5468 6520 }|(r0m).. The \n+00016050: 7365 636f 6e64 2064 7261 7769 6e67 2075 second drawing u\n+00016060: 7365 7320 7468 6520 7361 6d65 2074 6563 ses the same tec\n+00016070: 686e 6971 7565 732e 2020 4f6e 6c79 2074 hniques. Only t\n+00016080: 6865 206d 6574 686f 6420 666f 720a 6472 he method for.dr\n+00016090: 6177 696e 6720 7468 6520 656c 6c69 7074 awing the ellipt\n+000160a0: 6963 616c 2061 7263 2069 7320 6e65 772e ical arc is new.\n+000160b0: 2020 4865 7265 2069 7320 7468 6520 636f Here is the co\n+000160c0: 6465 2e0a 2020 6465 6620 6d69 6420 2828 de.. def mid ((\n+000160d0: 7030 3029 2d28 4f29 2b28 7031 3029 2d28 p00)-(O)+(p10)-(\n+000160e0: 4f29 2b28 7031 3129 2d28 4f29 2b28 7030 O)+(p11)-(O)+(p0\n+000160f0: 3129 2d28 4f29 292f 342b 284f 290a 2020 1)-(O))/4+(O). \n+00016100: 7370 6563 6961 6c7c 5c72 7075 7423 317b special|\\rput#1{\n+00016110: 5c70 7363 7573 746f 6d7b 0a20 2020 205c \\pscustom{. \\\n+00016120: 7363 616c 657b 3120 312e 337d 0a20 2020 scale{1 1.3}. \n+00016130: 205c 7073 6172 635b 6172 726f 776c 656e \\psarc[arrowlen\n+00016140: 6774 683d 2e35 5d7b 2d3e 7d7b 2e32 357d gth=.5]{->}{.25}\n+00016150: 7b2d 3630 7d7b 3234 307d 7d7d 7c0a 2020 {-60}{240}}}|. \n+00016160: 2020 5b6c 6179 3d6f 7665 725d 286d 6964 [lay=over](mid\n+00016170: 290a 5765 2063 6f75 6c64 2068 6176 6520 ).We could have \n+00016180: 7377 6570 7420 6120 706f 696e 7420 746f swept a point to\n+00016190: 206d 616b 6520 7468 6520 6172 6320 7769 make the arc wi\n+000161a0: 7468 20e2 8098 736b 6574 6368 e280 992c th ...sketch...,\n+000161b0: 2062 7574 2075 7369 6e67 2061 0ae2 8098 but using a....\n+000161c0: 5053 5472 6963 6b73 e280 9920 6375 7374 PSTricks... cust\n+000161d0: 6f6d 2067 7261 7068 6963 2077 6173 2073 om graphic was s\n+000161e0: 696d 706c 6572 2e20 2041 6761 696e 2077 impler. Again w\n+000161f0: 6520 636f 6d70 7574 6564 2074 6865 2063 e computed the c\n+00016200: 656e 7472 6f69 640a 6f66 2074 6865 2071 entroid.of the q\n+00016210: 7561 6472 696c 6174 6572 616c 2062 7920 uadrilateral by \n+00016220: 6176 6572 6167 696e 6720 706f 696e 7473 averaging points\n+00016230: 2e20 204e 6f74 6520 7468 6174 2073 6361 . Note that sca\n+00016240: 6c69 6e67 2069 6e0a 506f 7374 7363 7269 ling in.Postscri\n+00016250: 7074 2064 6973 746f 7274 7320 7468 6520 pt distorts the \n+00016260: 6172 726f 7768 6561 642c 2062 7574 2069 arrowhead, but i\n+00016270: 6e20 7468 6973 2063 6173 6520 7468 6520 n this case the \n+00016280: 6469 7374 6f72 7469 6f6e 0a61 6374 7561 distortion.actua\n+00016290: 6c6c 7920 6c6f 6f6b 7320 6265 7474 6572 lly looks better\n+000162a0: 2069 6e20 7468 6520 7072 6f6a 6563 7469 in the projecti\n+000162b0: 6f6e 206f 6620 7468 6520 736c 616e 7465 on of the slante\n+000162c0: 6420 6661 6365 2e20 2041 20e2 8098 736b d face. A ...sk\n+000162d0: 6574 6368 e280 990a 6172 726f 7768 6561 etch....arrowhea\n+000162e0: 6420 776f 756c 6420 6e6f 7420 6861 7665 d would not have\n+000162f0: 2062 6565 6e20 6469 7374 6f72 7465 642e been distorted.\n+00016300: 0a0a 2020 2054 6865 2063 6f6d 706c 6574 .. The complet\n+00016310: 6520 636f 6465 2066 6f72 2074 6869 7320 e code for this \n+00016320: 6578 616d 706c 652c 2077 6869 6368 2064 example, which d\n+00016330: 7261 7773 2065 6974 6865 7220 6669 6775 raws either figu\n+00016340: 7265 0a64 6570 656e 6469 6e67 206f 6e20 re.depending on \n+00016350: 7468 6520 6465 6669 6e69 7469 6f6e 206f the definition o\n+00016360: 6620 7468 6520 7461 6720 e280 983c 6c61 f the tag ......, is in\n+00016380: 636c 7564 6564 2069 6e20 7468 650a e280 cluded in the...\n+00016390: 9873 6b65 7463 68e2 8099 2064 6973 7472 .sketch... distr\n+000163a0: 6962 7574 696f 6e20 696e 2074 6865 2066 ibution in the f\n+000163b0: 696c 6520 e280 9874 7275 6e63 6174 6564 ile ...truncated\n+000163c0: 636f 6e65 2e73 6be2 8099 2e0a 0a1f 0a46 cone.sk........F\n+000163d0: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+000163e0: 2c20 204e 6f64 653a 2041 2068 6965 7261 , Node: A hiera\n+000163f0: 7263 6869 6361 6c20 6d6f 6465 6c2c 2020 rchical model, \n+00016400: 4e65 7874 3a20 4361 7665 6174 732c 2020 Next: Caveats, \n+00016410: 5072 6576 3a20 4120 7465 6368 6e69 6361 Prev: A technica\n+00016420: 6c20 6472 6177 696e 672c 2020 5570 3a20 l drawing, Up: \n+00016430: 4275 696c 6469 6e67 2061 2064 7261 7769 Building a drawi\n+00016440: 6e67 0a0a 342e 3320 4120 6869 6572 6172 ng..4.3 A hierar\n+00016450: 6368 6963 616c 206d 6f64 656c 0a3d 3d3d chical model.===\n 00016460: 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d 3d3d ================\n-00016470: 3d3d 3d3d 3d3d 3d0a 0a57 6869 6c65 20e2 =======..While .\n-00016480: 8098 736b 6574 6368 e280 9920 7761 7320 ..sketch... was \n-00016490: 6e65 7665 7220 6d65 616e 7420 746f 2062 never meant to b\n-000164a0: 6520 6120 6765 6f6d 6574 7269 6320 6d6f e a geometric mo\n-000164b0: 6465 6c69 6e67 206c 616e 6775 6167 652c deling language,\n-000164c0: 2069 740a 636f 6d65 7320 6661 6972 6c79 it.comes fairly\n-000164d0: 2063 6c6f 7365 2e20 2054 6865 2066 6f6c close. The fol\n-000164e0: 6c6f 7769 6e67 2065 7861 6d70 6c65 2070 lowing example p\n-000164f0: 7574 7320 616c 6c20 7765 2068 6176 6520 uts all we have \n-00016500: 7365 656e 2074 6f20 776f 726b 0a69 6e20 seen to work.in \n-00016510: 6120 7665 7279 2073 696d 706c 6520 6d6f a very simple mo\n-00016520: 6465 6c20 6f66 2074 6865 2068 756d 616e del of the human\n-00016530: 2068 616e 642e 2020 5374 6172 7420 6279 hand. Start by\n-00016540: 2073 7765 6570 696e 6720 6120 6c69 6e65 sweeping a line\n-00016550: 2074 6f0a 6d61 6b65 2061 2074 7275 6e63 to.make a trunc\n-00016560: 6174 6564 2063 6f6e 652c 2077 6869 6368 ated cone, which\n-00016570: 2077 696c 6c20 6265 2063 6f70 6965 6420 will be copied \n-00016580: 6f76 6572 2061 6e64 206f 7665 7220 6167 over and over ag\n-00016590: 6169 6e20 746f 206d 616b 650a 7468 6520 ain to make.the \n-000165a0: 7365 676d 656e 7473 206f 6620 6669 6e67 segments of fing\n-000165b0: 6572 732e 0a20 2064 6566 204f 2028 302c ers.. def O (0,\n-000165c0: 302c 3029 2025 206f 7269 6769 6e0a 2020 0,0) % origin. \n-000165d0: 6465 6620 4920 5b31 2c30 2c30 5d20 6465 def I [1,0,0] de\n-000165e0: 6620 4a20 5b30 2c31 2c30 5d20 6465 6620 f J [0,1,0] def \n-000165f0: 4b20 5b30 2c30 2c31 5d20 2520 6361 6e6f K [0,0,1] % cano\n-00016600: 6e69 6361 6c20 756e 6974 2076 6563 746f nical unit vecto\n-00016610: 7273 0a20 2064 6566 2073 6567 6d65 6e74 rs. def segment\n-00016620: 207b 0a20 2020 2064 6566 206e 5f66 6163 {. def n_fac\n-00016630: 6573 2038 0a20 2020 2073 7765 6570 207b es 8. sweep {\n-00016640: 206e 5f66 6163 6573 3c3e 2c20 726f 7461 n_faces<>, rota\n-00016650: 7465 2833 3630 202f 206e 5f66 6163 6573 te(360 / n_faces\n-00016660: 2c20 5b4a 5d29 207d 200a 2020 2020 2020 , [J]) } . \n-00016670: 6c69 6e65 2870 726f 7869 6d61 6c5f 7261 line(proximal_ra\n-00016680: 642c 2030 2928 6469 7374 616c 5f72 6164 d, 0)(distal_rad\n-00016690: 2c20 6469 7374 616c 5f6c 656e 290a 2020 , distal_len). \n-000166a0: 7d0a 496e 2068 616e 6420 616e 6174 6f6d }.In hand anatom\n-000166b0: 792c 205f 6469 7374 616c 5f20 6973 2022 y, _distal_ is \"\n-000166c0: 6174 2074 6865 2074 6970 2220 616e 6420 at the tip\" and \n-000166d0: 5f70 726f 7869 6d61 6c5f 2069 7320 2269 _proximal_ is \"i\n-000166e0: 6e20 7468 6520 6172 6561 0a6f 6620 7468 n the area.of th\n-000166f0: 6520 7061 6c6d 2e22 2020 5765 2068 6176 e palm.\" We hav\n-00016700: 6520 6f6d 6974 7465 6420 616c 6c20 7468 e omitted all th\n-00016710: 6520 7363 616c 6172 2063 6f6e 7374 616e e scalar constan\n-00016720: 7473 2e20 2059 6f75 2063 616e 2066 696e ts. You can fin\n-00016730: 640a 7468 656d 2069 6e20 e280 9868 616e d.them in ...han\n-00016740: 642e 736b e280 992c 2077 6869 6368 2069 d.sk..., which i\n-00016750: 7320 7072 6f76 6964 6564 2069 6e20 7468 s provided in th\n-00016760: 6520 e280 9873 6b65 7463 68e2 8099 2064 e ...sketch... d\n-00016770: 6973 7472 6962 7574 696f 6e2e 0a0a 2020 istribution... \n-00016780: 2057 6520 616c 736f 206e 6565 6420 6120 We also need a \n-00016790: 7072 6f74 6f74 7970 6963 616c 2073 7068 prototypical sph\n-000167a0: 6572 6520 746f 2075 7365 2066 6f72 2074 ere to use for t\n-000167b0: 6865 206a 6f69 6e74 7320 7468 656d 7365 he joints themse\n-000167c0: 6c76 6573 2e0a 2020 6465 6620 6a6f 696e lves.. def join\n-000167d0: 745f 7370 6865 7265 207b 0a20 2020 2064 t_sphere {. d\n-000167e0: 6566 206e 5f6a 6f69 6e74 5f66 6163 6573 ef n_joint_faces\n-000167f0: 2038 0a20 2020 2073 7765 6570 205b 6669 8. sweep [fi\n-00016800: 6c6c 636f 6c6f 723d 7265 645d 207b 206e llcolor=red] { n\n-00016810: 5f6a 6f69 6e74 5f66 6163 6573 2c20 726f _joint_faces, ro\n-00016820: 7461 7465 2833 3630 202f 206e 5f6a 6f69 tate(360 / n_joi\n-00016830: 6e74 5f66 6163 6573 2c20 5b4a 5d29 207d nt_faces, [J]) }\n-00016840: 0a20 2020 2020 2073 7765 6570 207b 206e . sweep { n\n-00016850: 5f6a 6f69 6e74 5f66 6163 6573 2c20 726f _joint_faces, ro\n-00016860: 7461 7465 2831 3830 202f 206e 5f6a 6f69 tate(180 / n_joi\n-00016870: 6e74 5f66 6163 6573 2920 7d20 0a20 2020 nt_faces) } . \n-00016880: 2020 2020 2028 302c 202d 6a6f 696e 745f (0, -joint_\n-00016890: 7261 6429 0a20 207d 0a0a 2020 2057 6527 rad). }.. We'\n-000168a0: 6c6c 206e 6f77 2064 6573 6967 6e20 7468 ll now design th\n-000168b0: 6520 696e 6465 7820 6669 6e67 6572 2028 e index finger (\n-000168c0: 6e75 6d62 6572 2031 2069 6e20 6f75 7220 number 1 in our \n-000168d0: 6e6f 7461 7469 6f6e 616c 0a63 6f6e 7665 notational.conve\n-000168e0: 6e74 696f 6e3b 2066 696e 6765 7220 3020 ntion; finger 0 \n-000168f0: 6973 2074 6865 2074 6875 6d62 292e 2020 is the thumb). \n-00016900: 5468 6520 6469 7374 616c 2072 6f74 6174 The distal rotat\n-00016910: 696f 6e20 666f 7220 7468 6520 6669 6e67 ion for the fing\n-00016920: 6572 0a61 7070 6c69 6573 206f 6e6c 7920 er.applies only \n-00016930: 746f 2074 6865 2074 6970 2c20 736f 2077 to the tip, so w\n-00016940: 6520 6465 6669 6e65 2074 6865 2066 6f6c e define the fol\n-00016950: 6c6f 7769 6e67 2e0a 2020 6465 6620 6469 lowing.. def di\n-00016960: 7374 616c 5f31 207b 0a20 2020 2070 7574 stal_1 {. put\n-00016970: 207b 2074 7261 6e73 6c61 7465 286a 6f69 { translate(joi\n-00016980: 6e74 5f67 6170 202a 206a 6f69 6e74 5f72 nt_gap * joint_r\n-00016990: 6164 202a 205b 4a5d 2920 0a20 2020 2020 ad * [J]) . \n-000169a0: 2020 2020 2074 6865 6e20 726f 7461 7465 then rotate\n-000169b0: 2864 6973 7461 6c5f 315f 726f 742c 205b (distal_1_rot, [\n-000169c0: 495d 2920 0a20 2020 2020 2020 2020 2074 I]) . t\n-000169d0: 6865 6e20 7472 616e 736c 6174 6528 2864 hen translate((d\n-000169e0: 6973 7461 6c5f 6c65 6e20 2b20 6a6f 696e istal_len + join\n-000169f0: 745f 6761 7020 2a20 6a6f 696e 745f 7261 t_gap * joint_ra\n-00016a00: 6429 202a 205b 4a5d 2920 7d0a 2020 2020 d) * [J]) }. \n-00016a10: 2020 7b73 6567 6d65 6e74 7d0a 2020 2020 {segment}. \n-00016a20: 7075 7420 7b20 726f 7461 7465 2864 6973 put { rotate(dis\n-00016a30: 7461 6c5f 315f 726f 7420 2f20 322c 205b tal_1_rot / 2, [\n-00016a40: 495d 290a 2020 2020 2020 2020 2020 7468 I]). th\n-00016a50: 656e 2074 7261 6e73 6c61 7465 2828 6469 en translate((di\n-00016a60: 7374 616c 5f6c 656e 202b 206a 6f69 6e74 stal_len + joint\n-00016a70: 5f67 6170 202a 206a 6f69 6e74 5f72 6164 _gap * joint_rad\n-00016a80: 2920 2a20 5b4a 5d29 207d 200a 2020 2020 ) * [J]) } . \n-00016a90: 2020 7b6a 6f69 6e74 5f73 7068 6572 657d {joint_sphere}\n-00016aa0: 0a20 2020 2070 7574 207b 2073 6361 6c65 . put { scale\n-00016ab0: 2820 5b4a 5d20 2b20 7072 6f78 696d 616c ( [J] + proximal\n-00016ac0: 5f64 6973 7461 6c5f 7261 7469 6f20 2a20 _distal_ratio * \n-00016ad0: 285b 495d 2b5b 4b5d 2920 2920 7d0a 2020 ([I]+[K]) ) }. \n-00016ae0: 2020 2020 7b73 6567 6d65 6e74 7d0a 2020 {segment}. \n-00016af0: 7d20 200a 5468 6520 6964 656e 7469 6669 } .The identifi\n-00016b00: 6572 7320 6865 7265 2061 7265 2066 6f72 ers here are for\n-00016b10: 2073 697a 6520 616e 6420 6c6f 6361 7469 size and locati\n-00016b20: 6f6e 2063 6f6e 7374 616e 7473 2e20 2054 on constants. T\n-00016b30: 6865 2065 7863 6570 7469 6f6e 0a69 7320 he exception.is \n-00016b40: e280 9864 6973 7461 6c5f 726f 745f 31e2 ...distal_rot_1.\n-00016b50: 8099 2e20 2054 6869 7320 726f 7461 7469 ... This rotati\n-00016b60: 6f6e 2070 6172 616d 6574 6572 206d 6f64 on parameter mod\n-00016b70: 656c 7320 7468 6520 666c 6578 696e 6720 els the flexing \n-00016b80: 6f66 2074 6865 0a66 696e 6765 7220 7469 of the.finger ti\n-00016b90: 702e 2020 5468 6520 6669 7273 7420 e280 p. The first ..\n-00016ba0: 9870 7574 e280 9920 6d61 6b65 7320 6120 .put... makes a \n-00016bb0: 636f 7079 206f 6620 7468 6520 6669 6e67 copy of the fing\n-00016bc0: 6572 2073 6567 6d65 6e74 2074 6861 7420 er segment that \n-00016bd0: 6973 0a74 7261 6e73 6c61 7465 6420 7570 is.translated up\n-00016be0: 7761 7264 206a 7573 7420 6661 7220 656e ward just far en\n-00016bf0: 6f75 6768 2074 6f20 6d61 6b65 2072 6f6f ough to make roo\n-00016c00: 6d20 666f 7220 7468 6520 7370 6865 7269 m for the spheri\n-00016c10: 6361 6c20 6a6f 696e 742e 0a54 6865 6e20 cal joint..Then \n-00016c20: 6974 2061 7070 6c69 6573 2074 6865 2064 it applies the d\n-00016c30: 6973 7461 6c20 726f 7461 7469 6f6e 2e20 istal rotation. \n-00016c40: 2046 696e 616c 6c79 2069 7420 7472 616e Finally it tran\n-00016c50: 736c 6174 6573 2074 6865 2077 686f 6c65 slates the whole\n-00016c60: 0a61 7373 656d 626c 7920 7570 7761 7264 .assembly upward\n-00016c70: 2061 6761 696e 2074 6f20 6d61 6b65 2072 again to make r\n-00016c80: 6f6f 6d20 666f 7220 7468 6520 6d69 6464 oom for the midd\n-00016c90: 6c65 2070 686c 616e 6765 7320 2874 6865 le phlanges (the\n-00016ca0: 206e 6578 740a 626f 6e65 2074 6f77 6172 next.bone towar\n-00016cb0: 6420 7468 6520 7061 6c6d 292e 2020 5468 d the palm). Th\n-00016cc0: 6520 7365 636f 6e64 20e2 8098 7075 74e2 e second ...put.\n-00016cd0: 8099 2070 6f73 6974 696f 6e73 2074 6865 .. positions the\n-00016ce0: 2073 7068 6572 652e 2020 5468 6572 6520 sphere. There \n-00016cf0: 6973 0a61 2072 6f74 6174 696f 6e20 746f is.a rotation to\n-00016d00: 2070 6c61 6365 2074 6865 2067 7269 6420 place the grid \n-00016d10: 6f6e 2074 6865 2073 7068 6572 6520 7375 on the sphere su\n-00016d20: 7266 6163 6520 6174 2061 6e20 6e69 6365 rface at an nice\n-00016d30: 2061 6e67 6c65 2c0a 7468 656e 2061 2074 angle,.then a t\n-00016d40: 7261 6e73 6c61 7469 6f6e 2074 6f20 7468 ranslation to th\n-00016d50: 6520 6261 7365 206f 6620 7468 6520 6469 e base of the di\n-00016d60: 7374 616c 2070 686c 616e 6765 732c 2077 stal phlanges, w\n-00016d70: 6869 6368 2069 7320 616c 736f 0a63 656e hich is also.cen\n-00016d80: 7465 7220 6f66 2069 7473 2072 6f74 6174 ter of its rotat\n-00016d90: 696f 6e2e 2020 4669 6e61 6c6c 792c 2074 ion. Finally, t\n-00016da0: 6865 206c 6173 7420 e280 9870 7574 e280 he last ...put..\n-00016db0: 9920 706f 7369 7469 6f6e 7320 7468 6520 . positions the \n-00016dc0: 6d69 6464 6c65 0a73 6567 6d65 6e74 2069 middle.segment i\n-00016dd0: 7473 656c 662e 0a0a 2020 2054 6865 206d tself... The m\n-00016de0: 6964 646c 6520 6a6f 696e 7420 6973 2074 iddle joint is t\n-00016df0: 6865 206e 6578 7420 6f6e 6520 646f 776e he next one down\n-00016e00: 2c20 7769 7468 2072 6f74 6174 696f 6e20 , with rotation \n-00016e10: 616e 676c 650a e280 986d 6964 646c 655f angle....middle_\n-00016e20: 726f 745f 31e2 8099 2e20 2057 6865 6e20 rot_1.... When \n-00016e30: 7468 6973 2061 6e67 6c65 2063 6861 6e67 this angle chang\n-00016e40: 6573 2c20 7765 206e 6565 6420 616c 6c20 es, we need all \n-00016e50: 7468 6520 6f62 6a65 6374 7320 696e 0ae2 the objects in..\n-00016e60: 8098 6469 7374 616c 5f31 e280 9920 746f ..distal_1... to\n-00016e70: 2072 6f74 6174 6520 6173 2061 2075 6e69 rotate as a uni\n-00016e80: 742e 2020 5468 6973 2069 7320 7468 6520 t. This is the \n-00016e90: 7265 6173 6f6e 696e 6720 6265 6869 6e64 reasoning behind\n-00016ea0: 2074 6865 206e 6578 740a 6465 6669 6e69 the next.defini\n-00016eb0: 7469 6f6e 2e0a 2020 6465 6620 6669 6e67 tion.. def fing\n-00016ec0: 6572 5f31 207b 0a20 2020 2070 7574 207b er_1 {. put {\n-00016ed0: 2074 7261 6e73 6c61 7465 286a 6f69 6e74 translate(joint\n-00016ee0: 5f67 6170 202a 206a 6f69 6e74 5f72 6164 _gap * joint_rad\n-00016ef0: 202a 205b 4a5d 290a 2020 2020 2020 2020 * [J]). \n-00016f00: 2020 7468 656e 2072 6f74 6174 6528 6d69 then rotate(mi\n-00016f10: 6464 6c65 5f31 5f72 6f74 2c20 5b49 5d29 ddle_1_rot, [I])\n-00016f20: 0a20 2020 2020 2020 2020 2074 6865 6e20 . then \n-00016f30: 7472 616e 736c 6174 6528 286d 6964 646c translate((middl\n-00016f40: 655f 7261 7469 6f20 2a20 6469 7374 616c e_ratio * distal\n-00016f50: 5f6c 656e 202b 200a 2020 2020 2020 2020 _len + . \n+00016470: 3d3d 3d3d 3d0a 0a57 6869 6c65 20e2 8098 =====..While ...\n+00016480: 736b 6574 6368 e280 9920 7761 7320 6e65 sketch... was ne\n+00016490: 7665 7220 6d65 616e 7420 746f 2062 6520 ver meant to be \n+000164a0: 6120 6765 6f6d 6574 7269 6320 6d6f 6465 a geometric mode\n+000164b0: 6c69 6e67 206c 616e 6775 6167 652c 2069 ling language, i\n+000164c0: 740a 636f 6d65 7320 6661 6972 6c79 2063 t.comes fairly c\n+000164d0: 6c6f 7365 2e20 2054 6865 2066 6f6c 6c6f lose. The follo\n+000164e0: 7769 6e67 2065 7861 6d70 6c65 2070 7574 wing example put\n+000164f0: 7320 616c 6c20 7765 2068 6176 6520 7365 s all we have se\n+00016500: 656e 2074 6f20 776f 726b 0a69 6e20 6120 en to work.in a \n+00016510: 7665 7279 2073 696d 706c 6520 6d6f 6465 very simple mode\n+00016520: 6c20 6f66 2074 6865 2068 756d 616e 2068 l of the human h\n+00016530: 616e 642e 2020 5374 6172 7420 6279 2073 and. Start by s\n+00016540: 7765 6570 696e 6720 6120 6c69 6e65 2074 weeping a line t\n+00016550: 6f0a 6d61 6b65 2061 2074 7275 6e63 6174 o.make a truncat\n+00016560: 6564 2063 6f6e 652c 2077 6869 6368 2077 ed cone, which w\n+00016570: 696c 6c20 6265 2063 6f70 6965 6420 6f76 ill be copied ov\n+00016580: 6572 2061 6e64 206f 7665 7220 6167 6169 er and over agai\n+00016590: 6e20 746f 206d 616b 650a 7468 6520 7365 n to make.the se\n+000165a0: 676d 656e 7473 206f 6620 6669 6e67 6572 gments of finger\n+000165b0: 732e 0a20 2064 6566 204f 2028 302c 302c s.. def O (0,0,\n+000165c0: 3029 2025 206f 7269 6769 6e0a 2020 6465 0) % origin. de\n+000165d0: 6620 4920 5b31 2c30 2c30 5d20 6465 6620 f I [1,0,0] def \n+000165e0: 4a20 5b30 2c31 2c30 5d20 6465 6620 4b20 J [0,1,0] def K \n+000165f0: 5b30 2c30 2c31 5d20 2520 6361 6e6f 6e69 [0,0,1] % canoni\n+00016600: 6361 6c20 756e 6974 2076 6563 746f 7273 cal unit vectors\n+00016610: 0a20 2064 6566 2073 6567 6d65 6e74 207b . def segment {\n+00016620: 0a20 2020 2064 6566 206e 5f66 6163 6573 . def n_faces\n+00016630: 2038 0a20 2020 2073 7765 6570 207b 206e 8. sweep { n\n+00016640: 5f66 6163 6573 3c3e 2c20 726f 7461 7465 _faces<>, rotate\n+00016650: 2833 3630 202f 206e 5f66 6163 6573 2c20 (360 / n_faces, \n+00016660: 5b4a 5d29 207d 200a 2020 2020 2020 6c69 [J]) } . li\n+00016670: 6e65 2870 726f 7869 6d61 6c5f 7261 642c ne(proximal_rad,\n+00016680: 2030 2928 6469 7374 616c 5f72 6164 2c20 0)(distal_rad, \n+00016690: 6469 7374 616c 5f6c 656e 290a 2020 7d0a distal_len). }.\n+000166a0: 496e 2068 616e 6420 616e 6174 6f6d 792c In hand anatomy,\n+000166b0: 205f 6469 7374 616c 5f20 6973 2022 6174 _distal_ is \"at\n+000166c0: 2074 6865 2074 6970 2220 616e 6420 5f70 the tip\" and _p\n+000166d0: 726f 7869 6d61 6c5f 2069 7320 2269 6e20 roximal_ is \"in \n+000166e0: 7468 6520 6172 6561 0a6f 6620 7468 6520 the area.of the \n+000166f0: 7061 6c6d 2e22 2020 5765 2068 6176 6520 palm.\" We have \n+00016700: 6f6d 6974 7465 6420 616c 6c20 7468 6520 omitted all the \n+00016710: 7363 616c 6172 2063 6f6e 7374 616e 7473 scalar constants\n+00016720: 2e20 2059 6f75 2063 616e 2066 696e 640a . You can find.\n+00016730: 7468 656d 2069 6e20 e280 9868 616e 642e them in ...hand.\n+00016740: 736b e280 992c 2077 6869 6368 2069 7320 sk..., which is \n+00016750: 7072 6f76 6964 6564 2069 6e20 7468 6520 provided in the \n+00016760: e280 9873 6b65 7463 68e2 8099 2064 6973 ...sketch... dis\n+00016770: 7472 6962 7574 696f 6e2e 0a0a 2020 2057 tribution... W\n+00016780: 6520 616c 736f 206e 6565 6420 6120 7072 e also need a pr\n+00016790: 6f74 6f74 7970 6963 616c 2073 7068 6572 ototypical spher\n+000167a0: 6520 746f 2075 7365 2066 6f72 2074 6865 e to use for the\n+000167b0: 206a 6f69 6e74 7320 7468 656d 7365 6c76 joints themselv\n+000167c0: 6573 2e0a 2020 6465 6620 6a6f 696e 745f es.. def joint_\n+000167d0: 7370 6865 7265 207b 0a20 2020 2064 6566 sphere {. def\n+000167e0: 206e 5f6a 6f69 6e74 5f66 6163 6573 2038 n_joint_faces 8\n+000167f0: 0a20 2020 2073 7765 6570 205b 6669 6c6c . sweep [fill\n+00016800: 636f 6c6f 723d 7265 645d 207b 206e 5f6a color=red] { n_j\n+00016810: 6f69 6e74 5f66 6163 6573 2c20 726f 7461 oint_faces, rota\n+00016820: 7465 2833 3630 202f 206e 5f6a 6f69 6e74 te(360 / n_joint\n+00016830: 5f66 6163 6573 2c20 5b4a 5d29 207d 0a20 _faces, [J]) }. \n+00016840: 2020 2020 2073 7765 6570 207b 206e 5f6a sweep { n_j\n+00016850: 6f69 6e74 5f66 6163 6573 2c20 726f 7461 oint_faces, rota\n+00016860: 7465 2831 3830 202f 206e 5f6a 6f69 6e74 te(180 / n_joint\n+00016870: 5f66 6163 6573 2920 7d20 0a20 2020 2020 _faces) } . \n+00016880: 2020 2028 302c 202d 6a6f 696e 745f 7261 (0, -joint_ra\n+00016890: 6429 0a20 207d 0a0a 2020 2057 6527 6c6c d). }.. We'll\n+000168a0: 206e 6f77 2064 6573 6967 6e20 7468 6520 now design the \n+000168b0: 696e 6465 7820 6669 6e67 6572 2028 6e75 index finger (nu\n+000168c0: 6d62 6572 2031 2069 6e20 6f75 7220 6e6f mber 1 in our no\n+000168d0: 7461 7469 6f6e 616c 0a63 6f6e 7665 6e74 tational.convent\n+000168e0: 696f 6e3b 2066 696e 6765 7220 3020 6973 ion; finger 0 is\n+000168f0: 2074 6865 2074 6875 6d62 292e 2020 5468 the thumb). Th\n+00016900: 6520 6469 7374 616c 2072 6f74 6174 696f e distal rotatio\n+00016910: 6e20 666f 7220 7468 6520 6669 6e67 6572 n for the finger\n+00016920: 0a61 7070 6c69 6573 206f 6e6c 7920 746f .applies only to\n+00016930: 2074 6865 2074 6970 2c20 736f 2077 6520 the tip, so we \n+00016940: 6465 6669 6e65 2074 6865 2066 6f6c 6c6f define the follo\n+00016950: 7769 6e67 2e0a 2020 6465 6620 6469 7374 wing.. def dist\n+00016960: 616c 5f31 207b 0a20 2020 2070 7574 207b al_1 {. put {\n+00016970: 2074 7261 6e73 6c61 7465 286a 6f69 6e74 translate(joint\n+00016980: 5f67 6170 202a 206a 6f69 6e74 5f72 6164 _gap * joint_rad\n+00016990: 202a 205b 4a5d 2920 0a20 2020 2020 2020 * [J]) . \n+000169a0: 2020 2074 6865 6e20 726f 7461 7465 2864 then rotate(d\n+000169b0: 6973 7461 6c5f 315f 726f 742c 205b 495d istal_1_rot, [I]\n+000169c0: 2920 0a20 2020 2020 2020 2020 2074 6865 ) . the\n+000169d0: 6e20 7472 616e 736c 6174 6528 2864 6973 n translate((dis\n+000169e0: 7461 6c5f 6c65 6e20 2b20 6a6f 696e 745f tal_len + joint_\n+000169f0: 6761 7020 2a20 6a6f 696e 745f 7261 6429 gap * joint_rad)\n+00016a00: 202a 205b 4a5d 2920 7d0a 2020 2020 2020 * [J]) }. \n+00016a10: 7b73 6567 6d65 6e74 7d0a 2020 2020 7075 {segment}. pu\n+00016a20: 7420 7b20 726f 7461 7465 2864 6973 7461 t { rotate(dista\n+00016a30: 6c5f 315f 726f 7420 2f20 322c 205b 495d l_1_rot / 2, [I]\n+00016a40: 290a 2020 2020 2020 2020 2020 7468 656e ). then\n+00016a50: 2074 7261 6e73 6c61 7465 2828 6469 7374 translate((dist\n+00016a60: 616c 5f6c 656e 202b 206a 6f69 6e74 5f67 al_len + joint_g\n+00016a70: 6170 202a 206a 6f69 6e74 5f72 6164 2920 ap * joint_rad) \n+00016a80: 2a20 5b4a 5d29 207d 200a 2020 2020 2020 * [J]) } . \n+00016a90: 7b6a 6f69 6e74 5f73 7068 6572 657d 0a20 {joint_sphere}. \n+00016aa0: 2020 2070 7574 207b 2073 6361 6c65 2820 put { scale( \n+00016ab0: 5b4a 5d20 2b20 7072 6f78 696d 616c 5f64 [J] + proximal_d\n+00016ac0: 6973 7461 6c5f 7261 7469 6f20 2a20 285b istal_ratio * ([\n+00016ad0: 495d 2b5b 4b5d 2920 2920 7d0a 2020 2020 I]+[K]) ) }. \n+00016ae0: 2020 7b73 6567 6d65 6e74 7d0a 2020 7d20 {segment}. } \n+00016af0: 200a 5468 6520 6964 656e 7469 6669 6572 .The identifier\n+00016b00: 7320 6865 7265 2061 7265 2066 6f72 2073 s here are for s\n+00016b10: 697a 6520 616e 6420 6c6f 6361 7469 6f6e ize and location\n+00016b20: 2063 6f6e 7374 616e 7473 2e20 2054 6865 constants. The\n+00016b30: 2065 7863 6570 7469 6f6e 0a69 7320 e280 exception.is ..\n+00016b40: 9864 6973 7461 6c5f 726f 745f 31e2 8099 .distal_rot_1...\n+00016b50: 2e20 2054 6869 7320 726f 7461 7469 6f6e . This rotation\n+00016b60: 2070 6172 616d 6574 6572 206d 6f64 656c parameter model\n+00016b70: 7320 7468 6520 666c 6578 696e 6720 6f66 s the flexing of\n+00016b80: 2074 6865 0a66 696e 6765 7220 7469 702e the.finger tip.\n+00016b90: 2020 5468 6520 6669 7273 7420 e280 9870 The first ...p\n+00016ba0: 7574 e280 9920 6d61 6b65 7320 6120 636f ut... makes a co\n+00016bb0: 7079 206f 6620 7468 6520 6669 6e67 6572 py of the finger\n+00016bc0: 2073 6567 6d65 6e74 2074 6861 7420 6973 segment that is\n+00016bd0: 0a74 7261 6e73 6c61 7465 6420 7570 7761 .translated upwa\n+00016be0: 7264 206a 7573 7420 6661 7220 656e 6f75 rd just far enou\n+00016bf0: 6768 2074 6f20 6d61 6b65 2072 6f6f 6d20 gh to make room \n+00016c00: 666f 7220 7468 6520 7370 6865 7269 6361 for the spherica\n+00016c10: 6c20 6a6f 696e 742e 0a54 6865 6e20 6974 l joint..Then it\n+00016c20: 2061 7070 6c69 6573 2074 6865 2064 6973 applies the dis\n+00016c30: 7461 6c20 726f 7461 7469 6f6e 2e20 2046 tal rotation. F\n+00016c40: 696e 616c 6c79 2069 7420 7472 616e 736c inally it transl\n+00016c50: 6174 6573 2074 6865 2077 686f 6c65 0a61 ates the whole.a\n+00016c60: 7373 656d 626c 7920 7570 7761 7264 2061 ssembly upward a\n+00016c70: 6761 696e 2074 6f20 6d61 6b65 2072 6f6f gain to make roo\n+00016c80: 6d20 666f 7220 7468 6520 6d69 6464 6c65 m for the middle\n+00016c90: 2070 686c 616e 6765 7320 2874 6865 206e phlanges (the n\n+00016ca0: 6578 740a 626f 6e65 2074 6f77 6172 6420 ext.bone toward \n+00016cb0: 7468 6520 7061 6c6d 292e 2020 5468 6520 the palm). The \n+00016cc0: 7365 636f 6e64 20e2 8098 7075 74e2 8099 second ...put...\n+00016cd0: 2070 6f73 6974 696f 6e73 2074 6865 2073 positions the s\n+00016ce0: 7068 6572 652e 2020 5468 6572 6520 6973 phere. There is\n+00016cf0: 0a61 2072 6f74 6174 696f 6e20 746f 2070 .a rotation to p\n+00016d00: 6c61 6365 2074 6865 2067 7269 6420 6f6e lace the grid on\n+00016d10: 2074 6865 2073 7068 6572 6520 7375 7266 the sphere surf\n+00016d20: 6163 6520 6174 2061 6e20 6e69 6365 2061 ace at an nice a\n+00016d30: 6e67 6c65 2c0a 7468 656e 2061 2074 7261 ngle,.then a tra\n+00016d40: 6e73 6c61 7469 6f6e 2074 6f20 7468 6520 nslation to the \n+00016d50: 6261 7365 206f 6620 7468 6520 6469 7374 base of the dist\n+00016d60: 616c 2070 686c 616e 6765 732c 2077 6869 al phlanges, whi\n+00016d70: 6368 2069 7320 616c 736f 0a63 656e 7465 ch is also.cente\n+00016d80: 7220 6f66 2069 7473 2072 6f74 6174 696f r of its rotatio\n+00016d90: 6e2e 2020 4669 6e61 6c6c 792c 2074 6865 n. Finally, the\n+00016da0: 206c 6173 7420 e280 9870 7574 e280 9920 last ...put... \n+00016db0: 706f 7369 7469 6f6e 7320 7468 6520 6d69 positions the mi\n+00016dc0: 6464 6c65 0a73 6567 6d65 6e74 2069 7473 ddle.segment its\n+00016dd0: 656c 662e 0a0a 2020 2054 6865 206d 6964 elf... The mid\n+00016de0: 646c 6520 6a6f 696e 7420 6973 2074 6865 dle joint is the\n+00016df0: 206e 6578 7420 6f6e 6520 646f 776e 2c20 next one down, \n+00016e00: 7769 7468 2072 6f74 6174 696f 6e20 616e with rotation an\n+00016e10: 676c 650a e280 986d 6964 646c 655f 726f gle....middle_ro\n+00016e20: 745f 31e2 8099 2e20 2057 6865 6e20 7468 t_1.... When th\n+00016e30: 6973 2061 6e67 6c65 2063 6861 6e67 6573 is angle changes\n+00016e40: 2c20 7765 206e 6565 6420 616c 6c20 7468 , we need all th\n+00016e50: 6520 6f62 6a65 6374 7320 696e 0ae2 8098 e objects in....\n+00016e60: 6469 7374 616c 5f31 e280 9920 746f 2072 distal_1... to r\n+00016e70: 6f74 6174 6520 6173 2061 2075 6e69 742e otate as a unit.\n+00016e80: 2020 5468 6973 2069 7320 7468 6520 7265 This is the re\n+00016e90: 6173 6f6e 696e 6720 6265 6869 6e64 2074 asoning behind t\n+00016ea0: 6865 206e 6578 740a 6465 6669 6e69 7469 he next.definiti\n+00016eb0: 6f6e 2e0a 2020 6465 6620 6669 6e67 6572 on.. def finger\n+00016ec0: 5f31 207b 0a20 2020 2070 7574 207b 2074 _1 {. put { t\n+00016ed0: 7261 6e73 6c61 7465 286a 6f69 6e74 5f67 ranslate(joint_g\n+00016ee0: 6170 202a 206a 6f69 6e74 5f72 6164 202a ap * joint_rad *\n+00016ef0: 205b 4a5d 290a 2020 2020 2020 2020 2020 [J]). \n+00016f00: 7468 656e 2072 6f74 6174 6528 6d69 6464 then rotate(midd\n+00016f10: 6c65 5f31 5f72 6f74 2c20 5b49 5d29 0a20 le_1_rot, [I]). \n+00016f20: 2020 2020 2020 2020 2074 6865 6e20 7472 then tr\n+00016f30: 616e 736c 6174 6528 286d 6964 646c 655f anslate((middle_\n+00016f40: 7261 7469 6f20 2a20 6469 7374 616c 5f6c ratio * distal_l\n+00016f50: 656e 202b 200a 2020 2020 2020 2020 2020 en + . \n 00016f60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00016f70: 2020 6a6f 696e 745f 6761 7020 2a20 6a6f joint_gap * jo\n-00016f80: 696e 745f 7261 6429 202a 205b 4a5d 2920 int_rad) * [J]) \n-00016f90: 7d0a 2020 2020 2020 7b64 6973 7461 6c5f }. {distal_\n-00016fa0: 317d 0a20 2020 2070 7574 207b 2073 6361 1}. put { sca\n-00016fb0: 6c65 2870 726f 7869 6d61 6c5f 6469 7374 le(proximal_dist\n-00016fc0: 616c 5f72 6174 696f 290a 2020 2020 2020 al_ratio). \n-00016fd0: 2020 2020 7468 656e 2072 6f74 6174 6528 then rotate(\n-00016fe0: 6d69 6464 6c65 5f31 5f72 6f74 202f 2032 middle_1_rot / 2\n-00016ff0: 2c20 5b49 5d29 0a20 2020 2020 2020 2020 , [I]). \n-00017000: 2074 6865 6e20 7472 616e 736c 6174 6528 then translate(\n-00017010: 286d 6964 646c 655f 7261 7469 6f20 2a20 (middle_ratio * \n-00017020: 6469 7374 616c 5f6c 656e 202b 200a 2020 distal_len + . \n+00016f70: 6a6f 696e 745f 6761 7020 2a20 6a6f 696e joint_gap * join\n+00016f80: 745f 7261 6429 202a 205b 4a5d 2920 7d0a t_rad) * [J]) }.\n+00016f90: 2020 2020 2020 7b64 6973 7461 6c5f 317d {distal_1}\n+00016fa0: 0a20 2020 2070 7574 207b 2073 6361 6c65 . put { scale\n+00016fb0: 2870 726f 7869 6d61 6c5f 6469 7374 616c (proximal_distal\n+00016fc0: 5f72 6174 696f 290a 2020 2020 2020 2020 _ratio). \n+00016fd0: 2020 7468 656e 2072 6f74 6174 6528 6d69 then rotate(mi\n+00016fe0: 6464 6c65 5f31 5f72 6f74 202f 2032 2c20 ddle_1_rot / 2, \n+00016ff0: 5b49 5d29 0a20 2020 2020 2020 2020 2074 [I]). t\n+00017000: 6865 6e20 7472 616e 736c 6174 6528 286d hen translate((m\n+00017010: 6964 646c 655f 7261 7469 6f20 2a20 6469 iddle_ratio * di\n+00017020: 7374 616c 5f6c 656e 202b 200a 2020 2020 stal_len + . \n 00017030: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00017040: 2020 2020 2020 2020 6a6f 696e 745f 6761 joint_ga\n-00017050: 7020 2a20 6a6f 696e 745f 7261 6429 202a p * joint_rad) *\n-00017060: 205b 4a5d 2920 7d20 0a20 2020 2020 207b [J]) } . {\n-00017070: 6a6f 696e 745f 7370 6865 7265 7d0a 2020 joint_sphere}. \n-00017080: 2020 7075 7420 7b20 7363 616c 6528 206d put { scale( m\n-00017090: 6964 646c 655f 7261 7469 6f20 2a20 5b4a iddle_ratio * [J\n-000170a0: 5d20 2b20 0a20 2020 2020 2020 2020 2020 ] + . \n-000170b0: 2020 2020 2020 7072 6f78 696d 616c 5f64 proximal_d\n-000170c0: 6973 7461 6c5f 7261 7469 6f5e 3220 2a20 istal_ratio^2 * \n-000170d0: 285b 495d 2b5b 4b5d 2920 2920 7d0a 2020 ([I]+[K]) ) }. \n-000170e0: 2020 2020 7b73 6567 6d65 6e74 7d0a 2020 {segment}. \n-000170f0: 7d0a 5468 6973 206c 6f6f 6b73 2076 6572 }.This looks ver\n-00017100: 7920 7369 6d69 6c61 7220 746f 2074 6865 y similar to the\n-00017110: 2070 7265 7669 6f75 7320 6465 6669 6e69 previous defini\n-00017120: 7469 6f6e 2c20 616e 6420 6974 2069 732e tion, and it is.\n-00017130: 2020 5468 650a 696d 706f 7274 616e 7420 The.important \n-00017140: 6469 6666 6572 656e 6365 2069 7320 7468 difference is th\n-00017150: 6174 2072 6174 6865 7220 7468 616e 2070 at rather than p\n-00017160: 6f73 6974 696f 6e69 6e67 2061 6e64 2072 ositioning and r\n-00017170: 6f74 6174 696e 6720 610a 7369 6e67 6c65 otating a.single\n-00017180: 2073 6567 6d65 6e74 2c20 7765 2070 6f73 segment, we pos\n-00017190: 6974 696f 6e20 616e 6420 726f 7461 7465 ition and rotate\n-000171a0: 2074 6865 2065 6e74 6972 6520 2261 7373 the entire \"ass\n-000171b0: 656d 626c 7922 2064 6566 696e 6564 2061 embly\" defined a\n-000171c0: 730a e280 9864 6973 7461 6c5f 31e2 8099 s....distal_1...\n-000171d0: 2e20 2054 6865 2072 6573 7420 6973 206a . The rest is j\n-000171e0: 7573 7420 6172 6974 686d 6574 6963 2074 ust arithmetic t\n-000171f0: 6f20 636f 6d70 7574 6520 7369 7a65 7320 o compute sizes \n-00017200: 616e 6420 706f 7369 7469 6f6e 730a 7468 and positions.th\n-00017210: 6174 206c 6f6f 6b20 6e69 6365 2e20 2054 at look nice. T\n-00017220: 6865 206c 6173 7420 e280 9870 7574 e280 he last ...put..\n-00017230: 9920 706c 6163 6573 2061 6e20 6170 7072 . places an appr\n-00017240: 6f70 7269 6174 656c 7920 7368 6170 6564 opriately shaped\n-00017250: 2073 6567 6d65 6e74 0a74 6861 7420 6973 segment.that is\n-00017260: 2074 6865 205f 7072 6f78 696d 616c 2070 the _proximal p\n-00017270: 686c 616e 6765 735f 2c20 7468 6520 626f hlanges_, the bo\n-00017280: 6e65 2074 6861 7420 6a6f 696e 7320 7468 ne that joins th\n-00017290: 6520 7061 6c6d 206f 6620 7468 650a 6861 e palm of the.ha\n-000172a0: 6e64 2e20 2054 6869 7320 636f 6d70 6c65 nd. This comple\n-000172b0: 7465 7320 7468 6520 6669 6e67 6572 2069 tes the finger i\n-000172c0: 7473 656c 662e 0a0a 2020 2041 6c6c 2074 tself... All t\n-000172d0: 6865 206f 7468 6572 2066 696e 6765 7273 he other fingers\n-000172e0: 2061 7265 2064 6573 6372 6962 6564 2069 are described i\n-000172f0: 6465 6e74 6963 616c 6c79 2074 6f20 7468 dentically to th\n-00017300: 6973 206f 6e65 2e20 2057 650a 6163 636f is one. We.acco\n-00017310: 756e 7420 666f 7220 7468 6520 6661 6374 unt for the fact\n-00017320: 2074 6861 7420 7265 616c 2066 696e 6765 that real finge\n-00017330: 7273 2061 7265 2064 6966 6665 7265 6e74 rs are different\n-00017340: 2073 697a 6573 2069 6e20 7468 6520 6e65 sizes in the ne\n-00017350: 7874 0a73 7465 702c 2077 6869 6368 2069 xt.step, which i\n-00017360: 7320 746f 2062 7569 6c64 2074 6865 2065 s to build the e\n-00017370: 6e74 6972 6520 6861 6e64 2e0a 0a20 2020 ntire hand... \n-00017380: 5468 6520 e280 9868 616e 64e2 8099 2064 The ...hand... d\n-00017390: 6566 696e 6974 696f 6e20 7468 6174 2066 efinition that f\n-000173a0: 6f6c 6c6f 7773 2069 6e63 6c75 6465 7320 ollows includes \n-000173b0: 6120 7365 6374 696f 6e20 666f 7220 6561 a section for ea\n-000173c0: 6368 0a66 696e 6765 722e 2020 5765 276c ch.finger. We'l\n-000173d0: 6c20 636f 6e74 696e 7565 2077 6974 6820 l continue with \n-000173e0: 6669 6e67 6572 2031 2061 6e64 206f 6d69 finger 1 and omi\n-000173f0: 7420 616c 6c20 7468 6520 6f74 6865 7273 t all the others\n-00017400: 2e20 2028 4f66 206e 6f74 650a 6973 2074 . (Of note.is t\n-00017410: 6861 7420 7468 6520 7468 756d 6220 6e65 hat the thumb ne\n-00017420: 6564 7320 736c 6967 6874 6c79 2073 7065 eds slightly spe\n-00017430: 6369 616c 2074 7265 6174 6d65 6e74 2d2d cial treatment--\n-00017440: 616e 2065 7874 7261 2072 6f74 6174 696f an extra rotatio\n-00017450: 6e20 746f 0a61 6363 6f75 6e74 2066 6f72 n to.account for\n-00017460: 2069 7473 206f 7070 6f73 696e 6720 616e its opposing an\n-00017470: 676c 652e 2020 5468 6973 2069 7320 636c gle. This is cl\n-00017480: 6561 7220 696e 2074 6865 2066 756c 6c20 ear in the full \n-00017490: 736f 7572 6365 2063 6f64 652e 290a 4e6f source code.).No\n-000174a0: 7420 7375 7270 7269 7369 6e67 6c79 2c20 t surprisingly, \n-000174b0: 7468 6520 e280 9868 616e 64e2 8099 2064 the ...hand... d\n-000174c0: 6566 696e 6974 696f 6e20 6c6f 6f6b 7320 efinition looks \n-000174d0: 7665 7279 206d 7563 6820 6c69 6b65 2074 very much like t\n-000174e0: 6865 0a70 7265 7669 6f75 7320 7477 6f2e he.previous two.\n-000174f0: 2020 4974 2073 686f 756c 6420 6265 206e It should be n\n-00017500: 6f20 7375 7270 7269 7365 2074 6861 7420 o surprise that \n-00017510: 7768 656e 2074 6865 2072 6f74 6174 696f when the rotatio\n-00017520: 6e20 7061 7261 6d65 7465 720a e280 986d n parameter....m\n-00017530: 6574 615f 315f 726f 74e2 8099 2063 6861 eta_1_rot... cha\n-00017540: 6e67 6573 2c20 7468 6520 656e 7469 7265 nges, the entire\n-00017550: 2066 696e 6765 7220 726f 7461 7465 7321 finger rotates!\n-00017560: 2020 5468 6572 6520 6973 2061 6e20 6164 There is an ad\n-00017570: 6469 7469 6f6e 616c 0a72 6f74 6174 696f ditional.rotatio\n-00017580: 6e20 7468 6174 2061 6c6c 6f77 7320 7468 n that allows th\n-00017590: 6520 6669 6e67 6572 7320 746f 2073 7072 e fingers to spr\n-000175a0: 6561 6420 6c61 7465 7261 6c6c 792e 2020 ead laterally. \n-000175b0: 5765 2073 6179 2074 6865 7365 0a6a 6f69 We say these.joi\n-000175c0: 6e74 7320 6f66 2074 6865 2070 726f 7869 nts of the proxi\n-000175d0: 6d61 6c20 7068 6c61 6e67 6573 2068 6176 mal phlanges hav\n-000175e0: 6520 7477 6f20 5f64 6567 7265 6573 206f e two _degrees o\n-000175f0: 6620 6672 6565 646f 6d5f 2e20 2054 6865 f freedom_. The\n-00017600: 0a6a 6f69 6e74 7320 6869 6768 6572 206f .joints higher o\n-00017610: 6e20 7468 6520 6669 6e67 6572 2068 6176 n the finger hav\n-00017620: 6520 6f6e 6c79 206f 6e65 2e20 2046 696e e only one. Fin\n-00017630: 616c 6c79 2c20 6561 6368 2066 696e 6765 ally, each finge\n-00017640: 7220 6973 0a73 6361 6c65 6420 6279 2061 r is.scaled by a\n-00017650: 2066 6163 746f 7220 746f 206c 656e 6420 factor to lend \n-00017660: 6974 2070 726f 706f 7274 696f 6e2e 0a20 it proportion.. \n-00017670: 2064 6566 2068 616e 6420 7b0a 2020 2020 def hand {. \n-00017680: 2520 6669 6e67 6572 2031 205b 616c 6c20 % finger 1 [all \n-00017690: 6f74 6865 7220 6669 6e67 6572 7320 6f6d other fingers om\n-000176a0: 6974 7465 645d 0a20 2020 2064 6566 2073 itted]. def s\n-000176b0: 6361 6c65 5f31 202e 3835 0a20 2020 2070 cale_1 .85. p\n-000176c0: 7574 207b 2073 6361 6c65 2873 6361 6c65 ut { scale(scale\n-000176d0: 5f31 2920 0a20 2020 2020 2020 2020 2074 _1) . t\n-000176e0: 6865 6e20 7472 616e 736c 6174 6528 286a hen translate((j\n-000176f0: 6f69 6e74 5f67 6170 202a 206a 6f69 6e74 oint_gap * joint\n-00017700: 5f72 6164 2920 2a20 5b4a 5d29 0a09 2020 _rad) * [J]).. \n-00017710: 7468 656e 2072 6f74 6174 6528 6d65 7461 then rotate(meta\n-00017720: 5f31 5f72 6f74 2c20 5b49 5d29 0a20 2020 _1_rot, [I]). \n-00017730: 2020 2020 2020 2074 6865 6e20 726f 7461 then rota\n-00017740: 7465 282d 7370 7265 6164 5f72 6f74 2c20 te(-spread_rot, \n-00017750: 5b4b 5d29 0a20 2020 2020 2020 2020 2074 [K]). t\n-00017760: 6865 6e20 7472 616e 736c 6174 6528 2870 hen translate((p\n-00017770: 726f 7869 6d61 6c5f 315f 6c6f 6329 202d roximal_1_loc) -\n-00017780: 2028 4f29 2920 7d20 0a20 2020 2020 207b (O)) } . {\n-00017790: 6669 6e67 6572 5f31 7d0a 2020 2020 7075 finger_1}. pu\n-000177a0: 7420 7b20 7363 616c 6528 7363 616c 655f t { scale(scale_\n-000177b0: 3120 2a20 7072 6f78 696d 616c 5f64 6973 1 * proximal_dis\n-000177c0: 7461 6c5f 7261 7469 6f5e 3229 0a20 2020 tal_ratio^2). \n-000177d0: 2020 2020 2020 2074 6865 6e20 726f 7461 then rota\n-000177e0: 7465 286d 6574 615f 315f 726f 7420 2f20 te(meta_1_rot / \n-000177f0: 322c 205b 495d 290a 2020 2020 2020 2020 2, [I]). \n-00017800: 2020 7468 656e 2072 6f74 6174 6528 2d73 then rotate(-s\n-00017810: 7072 6561 645f 726f 742c 205b 4b5d 290a pread_rot, [K]).\n-00017820: 2020 2020 2020 2020 2020 7468 656e 2074 then t\n-00017830: 7261 6e73 6c61 7465 2828 7072 6f78 696d ranslate((proxim\n-00017840: 616c 5f31 5f6c 6f63 2920 2d20 284f 2929 al_1_loc) - (O))\n-00017850: 207d 200a 2020 2020 2020 7b6a 6f69 6e74 } . {joint\n-00017860: 5f73 7068 6572 657d 0a0a 2020 2020 2520 _sphere}.. % \n-00017870: 7061 6c6d 0a20 2020 2073 7765 6570 207b palm. sweep {\n-00017880: 2031 2c20 726f 7461 7465 2836 2c20 2830 1, rotate(6, (0\n-00017890: 2c31 352c 3029 2c20 5b49 5d29 207d 0a20 ,15,0), [I]) }. \n-000178a0: 2020 2020 2070 7574 207b 2072 6f74 6174 put { rotat\n-000178b0: 6528 2d33 2c20 2830 2c31 352c 3029 2c20 e(-3, (0,15,0), \n-000178c0: 5b49 5d29 207d 207b 0a20 2020 2020 2020 [I]) } {. \n-000178d0: 2070 6f6c 7967 6f6e 2870 726f 7869 6d61 polygon(proxima\n-000178e0: 6c5f 315f 6c6f 6329 2870 726f 7869 6d61 l_1_loc)(proxima\n-000178f0: 6c5f 325f 6c6f 6329 0a20 2020 2020 2020 l_2_loc). \n-00017900: 2020 2020 2020 2020 2870 726f 7869 6d61 (proxima\n-00017910: 6c5f 335f 6c6f 6329 2870 726f 7869 6d61 l_3_loc)(proxima\n-00017920: 6c5f 345f 6c6f 6329 0a20 2020 2020 2020 l_4_loc). \n-00017930: 2020 2020 2020 2020 2868 3529 2868 3629 (h5)(h6)\n-00017940: 2868 3661 2928 6839 2928 6831 3029 0a20 (h6a)(h9)(h10). \n-00017950: 2020 2020 2020 2070 6f6c 7967 6f6e 2868 polygon(h\n-00017960: 3661 2928 6837 2928 6838 2928 6839 290a 6a)(h7)(h8)(h9).\n-00017970: 2020 207d 2020 7d0a 5468 6520 6c61 7374 } }.The last\n-00017980: 2073 6563 7469 6f6e 206f 6620 7468 6520 section of the \n-00017990: 6465 6669 6e69 7469 6f6e 2063 7265 6174 definition creat\n-000179a0: 6573 2074 6865 2070 6f6c 7974 6f70 6520 es the polytope \n-000179b0: 666f 7220 7468 6520 7061 6c6d 206f 660a for the palm of.\n-000179c0: 7468 6520 6861 6e64 2062 7920 e280 9873 the hand by ...s\n-000179d0: 7765 6570 e280 9969 6e67 2061 2031 302d weep...ing a 10-\n-000179e0: 7369 6465 6420 706f 6c79 676f 6e20 7468 sided polygon th\n-000179f0: 726f 7567 6820 6120 7665 7279 2073 686f rough a very sho\n-00017a00: 7274 2061 7263 0a28 3920 6465 6772 6565 rt arc.(9 degree\n-00017a10: 7329 2e20 2054 6869 7320 7072 6f76 6964 s). This provid\n-00017a20: 6573 2061 2077 6564 6765 2d73 6861 7065 es a wedge-shape\n-00017a30: 6420 7072 6f66 696c 6520 7768 656e 2076 d profile when v\n-00017a40: 6965 7765 6420 6672 6f6d 2074 6865 0a73 iewed from the.s\n-00017a50: 6964 652e 2020 5468 6520 7468 6963 6b20 ide. The thick \n-00017a60: 656e 6420 6f66 2074 6865 2077 6564 6765 end of the wedge\n-00017a70: 2069 7320 7468 6520 7772 6973 742e 2020 is the wrist. \n-00017a80: 4265 6361 7573 6520 7468 6520 706f 6c79 Because the poly\n-00017a90: 676f 6e20 6973 0a63 6f6e 6361 7665 2c20 gon is.concave, \n-00017aa0: 6974 2069 7320 7370 6c69 7420 696e 746f it is split into\n-00017ab0: 2069 6e74 6f20 7477 6f20 636f 6e76 6578 into two convex\n-00017ac0: 2073 6861 7065 7320 7769 7468 206e 696e shapes with nin\n-00017ad0: 6520 616e 6420 666f 7572 0a76 6572 7469 e and four.verti\n-00017ae0: 6365 732e 0a0a 2020 2057 6520 6361 6e20 ces... We can \n-00017af0: 6e6f 7720 6861 7665 2066 756e 2070 6f73 now have fun pos\n-00017b00: 6974 696f 6e69 6e67 2074 6865 2068 616e itioning the han\n-00017b10: 6420 6279 2061 646a 7573 7469 6e67 2074 d by adjusting t\n-00017b20: 6865 2076 6172 696f 7573 0a72 6f74 6174 he various.rotat\n-00017b30: 696f 6e20 616e 676c 6573 2e20 2054 6865 ion angles. The\n-00017b40: 2063 6f6d 706c 6574 6520 736f 7572 6365 complete source\n-00017b50: 2069 6e63 6c75 6465 7320 6465 6669 6e69 includes defini\n-00017b60: 7469 6f6e 7320 7769 7468 0a61 6c74 6572 tions with.alter\n-00017b70: 6e61 7469 7665 7320 7468 6174 2069 6e63 natives that inc\n-00017b80: 6c75 6465 2074 6865 2066 6f6c 6c6f 7769 lude the followi\n-00017b90: 6e67 2076 6965 7773 2061 6e64 206d 6f72 ng views and mor\n-00017ba0: 652e 0a0a 0008 5b69 6d61 6765 2073 7263 e.....[image src\n-00017bb0: 3d22 6578 3231 302e 706e 6722 2074 6578 =\"ex210.png\" tex\n-00017bc0: 743d 2249 6d61 6765 2065 7832 3130 206f t=\"Image ex210 o\n-00017bd0: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n-00017be0: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n-00017bf0: 6f63 756d 656e 742e 2200 085d 0008 5b69 ocument.\"..]..[i\n-00017c00: 6d61 6765 2073 7263 3d22 6578 3232 302e mage src=\"ex220.\n-00017c10: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n-00017c20: 2065 7832 3230 206f 6d69 7474 6564 2069 ex220 omitted i\n-00017c30: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n-00017c40: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n-00017c50: 2200 085d 0008 5b69 6d61 6765 2073 7263 \"..]..[image src\n-00017c60: 3d22 6578 3233 302e 706e 6722 2074 6578 =\"ex230.png\" tex\n-00017c70: 743d 2249 6d61 6765 2065 7832 3330 206f t=\"Image ex230 o\n-00017c80: 6d69 7474 6564 2069 6e20 7465 7874 2076 mitted in text v\n-00017c90: 6572 7369 6f6e 206f 6620 7468 6973 2064 ersion of this d\n-00017ca0: 6f63 756d 656e 742e 2200 085d 0008 5b69 ocument.\"..]..[i\n-00017cb0: 6d61 6765 2073 7263 3d22 6578 3234 302e mage src=\"ex240.\n-00017cc0: 706e 6722 2074 6578 743d 2249 6d61 6765 png\" text=\"Image\n-00017cd0: 2065 7832 3430 206f 6d69 7474 6564 2069 ex240 omitted i\n-00017ce0: 6e20 7465 7874 2076 6572 7369 6f6e 206f n text version o\n-00017cf0: 6620 7468 6973 2064 6f63 756d 656e 742e f this document.\n-00017d00: 2200 085d 0a0a 1f0a 4669 6c65 3a20 736b \"..]....File: sk\n-00017d10: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n-00017d20: 3a20 4361 7665 6174 732c 2020 5072 6576 : Caveats, Prev\n-00017d30: 3a20 4120 6869 6572 6172 6368 6963 616c : A hierarchical\n-00017d40: 206d 6f64 656c 2c20 2055 703a 2042 7569 model, Up: Bui\n-00017d50: 6c64 696e 6720 6120 6472 6177 696e 670a lding a drawing.\n-00017d60: 0a34 2e34 2043 6176 6561 7473 0a3d 3d3d .4.4 Caveats.===\n-00017d70: 3d3d 3d3d 3d3d 3d3d 0a0a e280 9853 6b65 ========.....Ske\n-00017d80: 7463 68e2 8099 2069 7320 6120 6661 6972 tch... is a fair\n-00017d90: 6c79 2070 6f77 6572 6675 6c20 746f 6f6c ly powerful tool\n-00017da0: 2066 6f72 2064 7261 7769 6e67 2c20 6275 for drawing, bu\n-00017db0: 742c 206a 7573 7420 6173 2077 6974 6820 t, just as with \n-00017dc0: 5465 582c 0a74 6865 2070 6f77 6572 2074 TeX,.the power t\n-00017dd0: 6f20 6372 6561 7465 2062 6561 7574 6966 o create beautif\n-00017de0: 756c 2072 6573 756c 7473 2063 6f6d 6573 ul results comes\n-00017df0: 2061 6c6f 6e67 2077 6974 6820 7468 6520 along with the \n-00017e00: 706f 7765 7220 746f 206d 616b 650a 6d69 power to make.mi\n-00017e10: 7374 616b 6573 2e20 2054 6865 2066 6f6c stakes. The fol\n-00017e20: 6c6f 7769 6e67 2061 7265 2073 6f6d 6520 lowing are some \n-00017e30: 706f 696e 7473 2077 6865 7265 2063 6172 points where car\n-00017e40: 6520 6973 206e 6563 6573 7361 7279 2061 e is necessary a\n-00017e50: 6e64 0a77 6865 7265 2074 6865 2063 7572 nd.where the cur\n-00017e60: 7265 6e74 2076 6572 7369 6f6e 206f 6620 rent version of \n-00017e70: e280 9873 6b65 7463 68e2 8099 2069 7320 ...sketch... is \n-00017e80: 6c69 6d69 7465 6420 6f72 2068 6173 206b limited or has k\n-00017e90: 6e6f 776e 2062 7567 732e 0a0a 2a20 4d65 nown bugs...* Me\n-00017ea0: 6e75 3a0a 0a2a 204c 696d 6974 7320 6f6e nu:..* Limits on\n-00017eb0: 2065 7272 6f72 2064 6574 6563 7469 6f6e error detection\n-00017ec0: 3a3a 2020 2057 6861 7420 736b 6574 6368 :: What sketch\n-00017ed0: 2064 6f65 736e 2774 2064 6f2e 0a2a 2043 doesn't do..* C\n-00017ee0: 6c69 7070 696e 673a 3a20 2020 2020 2020 lipping:: \n-00017ef0: 2020 2020 2020 2020 2020 2020 204e 6f20 No \n-00017f00: 636c 6970 7069 6e67 2061 7420 7072 6573 clipping at pres\n-00017f10: 656e 742e 0a2a 2048 6964 6465 6e20 7375 ent..* Hidden su\n-00017f20: 7266 6163 6520 7265 6d6f 7661 6c3a 3a20 rface removal:: \n-00017f30: 2020 2020 2049 6d70 6572 6665 6374 696f Imperfectio\n-00017f40: 6e73 2074 6f20 6669 782e 0a0a 1f0a 4669 ns to fix.....Fi\n-00017f50: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n-00017f60: 2020 4e6f 6465 3a20 4c69 6d69 7473 206f Node: Limits o\n-00017f70: 6e20 6572 726f 7220 6465 7465 6374 696f n error detectio\n-00017f80: 6e2c 2020 4e65 7874 3a20 436c 6970 7069 n, Next: Clippi\n-00017f90: 6e67 2c20 2050 7265 763a 2043 6176 6561 ng, Prev: Cavea\n-00017fa0: 7473 2c20 2055 703a 2043 6176 6561 7473 ts, Up: Caveats\n-00017fb0: 0a0a 342e 342e 3120 4c69 6d69 7473 206f ..4.4.1 Limits o\n-00017fc0: 6e20 e280 9873 6b65 7463 68e2 8099 2065 n ...sketch... e\n-00017fd0: 7272 6f72 2064 6574 6563 7469 6f6e 0a2d rror detection.-\n+00017040: 2020 2020 2020 6a6f 696e 745f 6761 7020 joint_gap \n+00017050: 2a20 6a6f 696e 745f 7261 6429 202a 205b * joint_rad) * [\n+00017060: 4a5d 2920 7d20 0a20 2020 2020 207b 6a6f J]) } . {jo\n+00017070: 696e 745f 7370 6865 7265 7d0a 2020 2020 int_sphere}. \n+00017080: 7075 7420 7b20 7363 616c 6528 206d 6964 put { scale( mid\n+00017090: 646c 655f 7261 7469 6f20 2a20 5b4a 5d20 dle_ratio * [J] \n+000170a0: 2b20 0a20 2020 2020 2020 2020 2020 2020 + . \n+000170b0: 2020 2020 7072 6f78 696d 616c 5f64 6973 proximal_dis\n+000170c0: 7461 6c5f 7261 7469 6f5e 3220 2a20 285b tal_ratio^2 * ([\n+000170d0: 495d 2b5b 4b5d 2920 2920 7d0a 2020 2020 I]+[K]) ) }. \n+000170e0: 2020 7b73 6567 6d65 6e74 7d0a 2020 7d0a {segment}. }.\n+000170f0: 5468 6973 206c 6f6f 6b73 2076 6572 7920 This looks very \n+00017100: 7369 6d69 6c61 7220 746f 2074 6865 2070 similar to the p\n+00017110: 7265 7669 6f75 7320 6465 6669 6e69 7469 revious definiti\n+00017120: 6f6e 2c20 616e 6420 6974 2069 732e 2020 on, and it is. \n+00017130: 5468 650a 696d 706f 7274 616e 7420 6469 The.important di\n+00017140: 6666 6572 656e 6365 2069 7320 7468 6174 fference is that\n+00017150: 2072 6174 6865 7220 7468 616e 2070 6f73 rather than pos\n+00017160: 6974 696f 6e69 6e67 2061 6e64 2072 6f74 itioning and rot\n+00017170: 6174 696e 6720 610a 7369 6e67 6c65 2073 ating a.single s\n+00017180: 6567 6d65 6e74 2c20 7765 2070 6f73 6974 egment, we posit\n+00017190: 696f 6e20 616e 6420 726f 7461 7465 2074 ion and rotate t\n+000171a0: 6865 2065 6e74 6972 6520 2261 7373 656d he entire \"assem\n+000171b0: 626c 7922 2064 6566 696e 6564 2061 730a bly\" defined as.\n+000171c0: e280 9864 6973 7461 6c5f 31e2 8099 2e20 ...distal_1.... \n+000171d0: 2054 6865 2072 6573 7420 6973 206a 7573 The rest is jus\n+000171e0: 7420 6172 6974 686d 6574 6963 2074 6f20 t arithmetic to \n+000171f0: 636f 6d70 7574 6520 7369 7a65 7320 616e compute sizes an\n+00017200: 6420 706f 7369 7469 6f6e 730a 7468 6174 d positions.that\n+00017210: 206c 6f6f 6b20 6e69 6365 2e20 2054 6865 look nice. The\n+00017220: 206c 6173 7420 e280 9870 7574 e280 9920 last ...put... \n+00017230: 706c 6163 6573 2061 6e20 6170 7072 6f70 places an approp\n+00017240: 7269 6174 656c 7920 7368 6170 6564 2073 riately shaped s\n+00017250: 6567 6d65 6e74 0a74 6861 7420 6973 2074 egment.that is t\n+00017260: 6865 205f 7072 6f78 696d 616c 2070 686c he _proximal phl\n+00017270: 616e 6765 735f 2c20 7468 6520 626f 6e65 anges_, the bone\n+00017280: 2074 6861 7420 6a6f 696e 7320 7468 6520 that joins the \n+00017290: 7061 6c6d 206f 6620 7468 650a 6861 6e64 palm of the.hand\n+000172a0: 2e20 2054 6869 7320 636f 6d70 6c65 7465 . This complete\n+000172b0: 7320 7468 6520 6669 6e67 6572 2069 7473 s the finger its\n+000172c0: 656c 662e 0a0a 2020 2041 6c6c 2074 6865 elf... All the\n+000172d0: 206f 7468 6572 2066 696e 6765 7273 2061 other fingers a\n+000172e0: 7265 2064 6573 6372 6962 6564 2069 6465 re described ide\n+000172f0: 6e74 6963 616c 6c79 2074 6f20 7468 6973 ntically to this\n+00017300: 206f 6e65 2e20 2057 650a 6163 636f 756e one. We.accoun\n+00017310: 7420 666f 7220 7468 6520 6661 6374 2074 t for the fact t\n+00017320: 6861 7420 7265 616c 2066 696e 6765 7273 hat real fingers\n+00017330: 2061 7265 2064 6966 6665 7265 6e74 2073 are different s\n+00017340: 697a 6573 2069 6e20 7468 6520 6e65 7874 izes in the next\n+00017350: 0a73 7465 702c 2077 6869 6368 2069 7320 .step, which is \n+00017360: 746f 2062 7569 6c64 2074 6865 2065 6e74 to build the ent\n+00017370: 6972 6520 6861 6e64 2e0a 0a20 2020 5468 ire hand... Th\n+00017380: 6520 e280 9868 616e 64e2 8099 2064 6566 e ...hand... def\n+00017390: 696e 6974 696f 6e20 7468 6174 2066 6f6c inition that fol\n+000173a0: 6c6f 7773 2069 6e63 6c75 6465 7320 6120 lows includes a \n+000173b0: 7365 6374 696f 6e20 666f 7220 6561 6368 section for each\n+000173c0: 0a66 696e 6765 722e 2020 5765 276c 6c20 .finger. We'll \n+000173d0: 636f 6e74 696e 7565 2077 6974 6820 6669 continue with fi\n+000173e0: 6e67 6572 2031 2061 6e64 206f 6d69 7420 nger 1 and omit \n+000173f0: 616c 6c20 7468 6520 6f74 6865 7273 2e20 all the others. \n+00017400: 2028 4f66 206e 6f74 650a 6973 2074 6861 (Of note.is tha\n+00017410: 7420 7468 6520 7468 756d 6220 6e65 6564 t the thumb need\n+00017420: 7320 736c 6967 6874 6c79 2073 7065 6369 s slightly speci\n+00017430: 616c 2074 7265 6174 6d65 6e74 2d2d 616e al treatment--an\n+00017440: 2065 7874 7261 2072 6f74 6174 696f 6e20 extra rotation \n+00017450: 746f 0a61 6363 6f75 6e74 2066 6f72 2069 to.account for i\n+00017460: 7473 206f 7070 6f73 696e 6720 616e 676c ts opposing angl\n+00017470: 652e 2020 5468 6973 2069 7320 636c 6561 e. This is clea\n+00017480: 7220 696e 2074 6865 2066 756c 6c20 736f r in the full so\n+00017490: 7572 6365 2063 6f64 652e 290a 4e6f 7420 urce code.).Not \n+000174a0: 7375 7270 7269 7369 6e67 6c79 2c20 7468 surprisingly, th\n+000174b0: 6520 e280 9868 616e 64e2 8099 2064 6566 e ...hand... def\n+000174c0: 696e 6974 696f 6e20 6c6f 6f6b 7320 7665 inition looks ve\n+000174d0: 7279 206d 7563 6820 6c69 6b65 2074 6865 ry much like the\n+000174e0: 0a70 7265 7669 6f75 7320 7477 6f2e 2020 .previous two. \n+000174f0: 4974 2073 686f 756c 6420 6265 206e 6f20 It should be no \n+00017500: 7375 7270 7269 7365 2074 6861 7420 7768 surprise that wh\n+00017510: 656e 2074 6865 2072 6f74 6174 696f 6e20 en the rotation \n+00017520: 7061 7261 6d65 7465 720a e280 986d 6574 parameter....met\n+00017530: 615f 315f 726f 74e2 8099 2063 6861 6e67 a_1_rot... chang\n+00017540: 6573 2c20 7468 6520 656e 7469 7265 2066 es, the entire f\n+00017550: 696e 6765 7220 726f 7461 7465 7321 2020 inger rotates! \n+00017560: 5468 6572 6520 6973 2061 6e20 6164 6469 There is an addi\n+00017570: 7469 6f6e 616c 0a72 6f74 6174 696f 6e20 tional.rotation \n+00017580: 7468 6174 2061 6c6c 6f77 7320 7468 6520 that allows the \n+00017590: 6669 6e67 6572 7320 746f 2073 7072 6561 fingers to sprea\n+000175a0: 6420 6c61 7465 7261 6c6c 792e 2020 5765 d laterally. We\n+000175b0: 2073 6179 2074 6865 7365 0a6a 6f69 6e74 say these.joint\n+000175c0: 7320 6f66 2074 6865 2070 726f 7869 6d61 s of the proxima\n+000175d0: 6c20 7068 6c61 6e67 6573 2068 6176 6520 l phlanges have \n+000175e0: 7477 6f20 5f64 6567 7265 6573 206f 6620 two _degrees of \n+000175f0: 6672 6565 646f 6d5f 2e20 2054 6865 0a6a freedom_. The.j\n+00017600: 6f69 6e74 7320 6869 6768 6572 206f 6e20 oints higher on \n+00017610: 7468 6520 6669 6e67 6572 2068 6176 6520 the finger have \n+00017620: 6f6e 6c79 206f 6e65 2e20 2046 696e 616c only one. Final\n+00017630: 6c79 2c20 6561 6368 2066 696e 6765 7220 ly, each finger \n+00017640: 6973 0a73 6361 6c65 6420 6279 2061 2066 is.scaled by a f\n+00017650: 6163 746f 7220 746f 206c 656e 6420 6974 actor to lend it\n+00017660: 2070 726f 706f 7274 696f 6e2e 0a20 2064 proportion.. d\n+00017670: 6566 2068 616e 6420 7b0a 2020 2020 2520 ef hand {. % \n+00017680: 6669 6e67 6572 2031 205b 616c 6c20 6f74 finger 1 [all ot\n+00017690: 6865 7220 6669 6e67 6572 7320 6f6d 6974 her fingers omit\n+000176a0: 7465 645d 0a20 2020 2064 6566 2073 6361 ted]. def sca\n+000176b0: 6c65 5f31 202e 3835 0a20 2020 2070 7574 le_1 .85. put\n+000176c0: 207b 2073 6361 6c65 2873 6361 6c65 5f31 { scale(scale_1\n+000176d0: 2920 0a20 2020 2020 2020 2020 2074 6865 ) . the\n+000176e0: 6e20 7472 616e 736c 6174 6528 286a 6f69 n translate((joi\n+000176f0: 6e74 5f67 6170 202a 206a 6f69 6e74 5f72 nt_gap * joint_r\n+00017700: 6164 2920 2a20 5b4a 5d29 0a09 2020 7468 ad) * [J]).. th\n+00017710: 656e 2072 6f74 6174 6528 6d65 7461 5f31 en rotate(meta_1\n+00017720: 5f72 6f74 2c20 5b49 5d29 0a20 2020 2020 _rot, [I]). \n+00017730: 2020 2020 2074 6865 6e20 726f 7461 7465 then rotate\n+00017740: 282d 7370 7265 6164 5f72 6f74 2c20 5b4b (-spread_rot, [K\n+00017750: 5d29 0a20 2020 2020 2020 2020 2074 6865 ]). the\n+00017760: 6e20 7472 616e 736c 6174 6528 2870 726f n translate((pro\n+00017770: 7869 6d61 6c5f 315f 6c6f 6329 202d 2028 ximal_1_loc) - (\n+00017780: 4f29 2920 7d20 0a20 2020 2020 207b 6669 O)) } . {fi\n+00017790: 6e67 6572 5f31 7d0a 2020 2020 7075 7420 nger_1}. put \n+000177a0: 7b20 7363 616c 6528 7363 616c 655f 3120 { scale(scale_1 \n+000177b0: 2a20 7072 6f78 696d 616c 5f64 6973 7461 * proximal_dista\n+000177c0: 6c5f 7261 7469 6f5e 3229 0a20 2020 2020 l_ratio^2). \n+000177d0: 2020 2020 2074 6865 6e20 726f 7461 7465 then rotate\n+000177e0: 286d 6574 615f 315f 726f 7420 2f20 322c (meta_1_rot / 2,\n+000177f0: 205b 495d 290a 2020 2020 2020 2020 2020 [I]). \n+00017800: 7468 656e 2072 6f74 6174 6528 2d73 7072 then rotate(-spr\n+00017810: 6561 645f 726f 742c 205b 4b5d 290a 2020 ead_rot, [K]). \n+00017820: 2020 2020 2020 2020 7468 656e 2074 7261 then tra\n+00017830: 6e73 6c61 7465 2828 7072 6f78 696d 616c nslate((proximal\n+00017840: 5f31 5f6c 6f63 2920 2d20 284f 2929 207d _1_loc) - (O)) }\n+00017850: 200a 2020 2020 2020 7b6a 6f69 6e74 5f73 . {joint_s\n+00017860: 7068 6572 657d 0a0a 2020 2020 2520 7061 phere}.. % pa\n+00017870: 6c6d 0a20 2020 2073 7765 6570 207b 2031 lm. sweep { 1\n+00017880: 2c20 726f 7461 7465 2836 2c20 2830 2c31 , rotate(6, (0,1\n+00017890: 352c 3029 2c20 5b49 5d29 207d 0a20 2020 5,0), [I]) }. \n+000178a0: 2020 2070 7574 207b 2072 6f74 6174 6528 put { rotate(\n+000178b0: 2d33 2c20 2830 2c31 352c 3029 2c20 5b49 -3, (0,15,0), [I\n+000178c0: 5d29 207d 207b 0a20 2020 2020 2020 2070 ]) } {. p\n+000178d0: 6f6c 7967 6f6e 2870 726f 7869 6d61 6c5f olygon(proximal_\n+000178e0: 315f 6c6f 6329 2870 726f 7869 6d61 6c5f 1_loc)(proximal_\n+000178f0: 325f 6c6f 6329 0a20 2020 2020 2020 2020 2_loc). \n+00017900: 2020 2020 2020 2870 726f 7869 6d61 6c5f (proximal_\n+00017910: 335f 6c6f 6329 2870 726f 7869 6d61 6c5f 3_loc)(proximal_\n+00017920: 345f 6c6f 6329 0a20 2020 2020 2020 2020 4_loc). \n+00017930: 2020 2020 2020 2868 3529 2868 3629 2868 (h5)(h6)(h\n+00017940: 3661 2928 6839 2928 6831 3029 0a20 2020 6a)(h9)(h10). \n+00017950: 2020 2020 2070 6f6c 7967 6f6e 2868 3661 polygon(h6a\n+00017960: 2928 6837 2928 6838 2928 6839 290a 2020 )(h7)(h8)(h9). \n+00017970: 207d 2020 7d0a 5468 6520 6c61 7374 2073 } }.The last s\n+00017980: 6563 7469 6f6e 206f 6620 7468 6520 6465 ection of the de\n+00017990: 6669 6e69 7469 6f6e 2063 7265 6174 6573 finition creates\n+000179a0: 2074 6865 2070 6f6c 7974 6f70 6520 666f the polytope fo\n+000179b0: 7220 7468 6520 7061 6c6d 206f 660a 7468 r the palm of.th\n+000179c0: 6520 6861 6e64 2062 7920 e280 9873 7765 e hand by ...swe\n+000179d0: 6570 e280 9969 6e67 2061 2031 302d 7369 ep...ing a 10-si\n+000179e0: 6465 6420 706f 6c79 676f 6e20 7468 726f ded polygon thro\n+000179f0: 7567 6820 6120 7665 7279 2073 686f 7274 ugh a very short\n+00017a00: 2061 7263 0a28 3920 6465 6772 6565 7329 arc.(9 degrees)\n+00017a10: 2e20 2054 6869 7320 7072 6f76 6964 6573 . This provides\n+00017a20: 2061 2077 6564 6765 2d73 6861 7065 6420 a wedge-shaped \n+00017a30: 7072 6f66 696c 6520 7768 656e 2076 6965 profile when vie\n+00017a40: 7765 6420 6672 6f6d 2074 6865 0a73 6964 wed from the.sid\n+00017a50: 652e 2020 5468 6520 7468 6963 6b20 656e e. The thick en\n+00017a60: 6420 6f66 2074 6865 2077 6564 6765 2069 d of the wedge i\n+00017a70: 7320 7468 6520 7772 6973 742e 2020 4265 s the wrist. Be\n+00017a80: 6361 7573 6520 7468 6520 706f 6c79 676f cause the polygo\n+00017a90: 6e20 6973 0a63 6f6e 6361 7665 2c20 6974 n is.concave, it\n+00017aa0: 2069 7320 7370 6c69 7420 696e 746f 2069 is split into i\n+00017ab0: 6e74 6f20 7477 6f20 636f 6e76 6578 2073 nto two convex s\n+00017ac0: 6861 7065 7320 7769 7468 206e 696e 6520 hapes with nine \n+00017ad0: 616e 6420 666f 7572 0a76 6572 7469 6365 and four.vertice\n+00017ae0: 732e 0a0a 2020 2057 6520 6361 6e20 6e6f s... We can no\n+00017af0: 7720 6861 7665 2066 756e 2070 6f73 6974 w have fun posit\n+00017b00: 696f 6e69 6e67 2074 6865 2068 616e 6420 ioning the hand \n+00017b10: 6279 2061 646a 7573 7469 6e67 2074 6865 by adjusting the\n+00017b20: 2076 6172 696f 7573 0a72 6f74 6174 696f various.rotatio\n+00017b30: 6e20 616e 676c 6573 2e20 2054 6865 2063 n angles. The c\n+00017b40: 6f6d 706c 6574 6520 736f 7572 6365 2069 omplete source i\n+00017b50: 6e63 6c75 6465 7320 6465 6669 6e69 7469 ncludes definiti\n+00017b60: 6f6e 7320 7769 7468 0a61 6c74 6572 6e61 ons with.alterna\n+00017b70: 7469 7665 7320 7468 6174 2069 6e63 6c75 tives that inclu\n+00017b80: 6465 2074 6865 2066 6f6c 6c6f 7769 6e67 de the following\n+00017b90: 2076 6965 7773 2061 6e64 206d 6f72 652e views and more.\n+00017ba0: 0a0a 0008 5b69 6d61 6765 2073 7263 3d22 ....[image src=\"\n+00017bb0: 6578 3231 302e 706e 6722 2074 6578 743d ex210.png\" text=\n+00017bc0: 2249 6d61 6765 2065 7832 3130 206f 6d69 \"Image ex210 omi\n+00017bd0: 7474 6564 2069 6e20 7465 7874 2076 6572 tted in text ver\n+00017be0: 7369 6f6e 206f 6620 7468 6973 2064 6f63 sion of this doc\n+00017bf0: 756d 656e 742e 2200 085d 0008 5b69 6d61 ument.\"..]..[ima\n+00017c00: 6765 2073 7263 3d22 6578 3232 302e 706e ge src=\"ex220.pn\n+00017c10: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+00017c20: 7832 3230 206f 6d69 7474 6564 2069 6e20 x220 omitted in \n+00017c30: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+00017c40: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+00017c50: 085d 0008 5b69 6d61 6765 2073 7263 3d22 .]..[image src=\"\n+00017c60: 6578 3233 302e 706e 6722 2074 6578 743d ex230.png\" text=\n+00017c70: 2249 6d61 6765 2065 7832 3330 206f 6d69 \"Image ex230 omi\n+00017c80: 7474 6564 2069 6e20 7465 7874 2076 6572 tted in text ver\n+00017c90: 7369 6f6e 206f 6620 7468 6973 2064 6f63 sion of this doc\n+00017ca0: 756d 656e 742e 2200 085d 0008 5b69 6d61 ument.\"..]..[ima\n+00017cb0: 6765 2073 7263 3d22 6578 3234 302e 706e ge src=\"ex240.pn\n+00017cc0: 6722 2074 6578 743d 2249 6d61 6765 2065 g\" text=\"Image e\n+00017cd0: 7832 3430 206f 6d69 7474 6564 2069 6e20 x240 omitted in \n+00017ce0: 7465 7874 2076 6572 7369 6f6e 206f 6620 text version of \n+00017cf0: 7468 6973 2064 6f63 756d 656e 742e 2200 this document.\".\n+00017d00: 085d 0a0a 1f0a 4669 6c65 3a20 736b 6574 .]....File: sket\n+00017d10: 6368 2e69 6e66 6f2c 2020 4e6f 6465 3a20 ch.info, Node: \n+00017d20: 4361 7665 6174 732c 2020 5072 6576 3a20 Caveats, Prev: \n+00017d30: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n+00017d40: 6f64 656c 2c20 2055 703a 2042 7569 6c64 odel, Up: Build\n+00017d50: 696e 6720 6120 6472 6177 696e 670a 0a34 ing a drawing..4\n+00017d60: 2e34 2043 6176 6561 7473 0a3d 3d3d 3d3d .4 Caveats.=====\n+00017d70: 3d3d 3d3d 3d3d 0a0a e280 9853 6b65 7463 ======.....Sketc\n+00017d80: 68e2 8099 2069 7320 6120 6661 6972 6c79 h... is a fairly\n+00017d90: 2070 6f77 6572 6675 6c20 746f 6f6c 2066 powerful tool f\n+00017da0: 6f72 2064 7261 7769 6e67 2c20 6275 742c or drawing, but,\n+00017db0: 206a 7573 7420 6173 2077 6974 6820 5465 just as with Te\n+00017dc0: 582c 0a74 6865 2070 6f77 6572 2074 6f20 X,.the power to \n+00017dd0: 6372 6561 7465 2062 6561 7574 6966 756c create beautiful\n+00017de0: 2072 6573 756c 7473 2063 6f6d 6573 2061 results comes a\n+00017df0: 6c6f 6e67 2077 6974 6820 7468 6520 706f long with the po\n+00017e00: 7765 7220 746f 206d 616b 650a 6d69 7374 wer to make.mist\n+00017e10: 616b 6573 2e20 2054 6865 2066 6f6c 6c6f akes. The follo\n+00017e20: 7769 6e67 2061 7265 2073 6f6d 6520 706f wing are some po\n+00017e30: 696e 7473 2077 6865 7265 2063 6172 6520 ints where care \n+00017e40: 6973 206e 6563 6573 7361 7279 2061 6e64 is necessary and\n+00017e50: 0a77 6865 7265 2074 6865 2063 7572 7265 .where the curre\n+00017e60: 6e74 2076 6572 7369 6f6e 206f 6620 e280 nt version of ..\n+00017e70: 9873 6b65 7463 68e2 8099 2069 7320 6c69 .sketch... is li\n+00017e80: 6d69 7465 6420 6f72 2068 6173 206b 6e6f mited or has kno\n+00017e90: 776e 2062 7567 732e 0a0a 2a20 4d65 6e75 wn bugs...* Menu\n+00017ea0: 3a0a 0a2a 204c 696d 6974 7320 6f6e 2065 :..* Limits on e\n+00017eb0: 7272 6f72 2064 6574 6563 7469 6f6e 3a3a rror detection::\n+00017ec0: 2020 2057 6861 7420 736b 6574 6368 2064 What sketch d\n+00017ed0: 6f65 736e 2774 2064 6f2e 0a2a 2043 6c69 oesn't do..* Cli\n+00017ee0: 7070 696e 673a 3a20 2020 2020 2020 2020 pping:: \n+00017ef0: 2020 2020 2020 2020 2020 204e 6f20 636c No cl\n+00017f00: 6970 7069 6e67 2061 7420 7072 6573 656e ipping at presen\n+00017f10: 742e 0a2a 2048 6964 6465 6e20 7375 7266 t..* Hidden surf\n+00017f20: 6163 6520 7265 6d6f 7661 6c3a 3a20 2020 ace removal:: \n+00017f30: 2020 2049 6d70 6572 6665 6374 696f 6e73 Imperfections\n+00017f40: 2074 6f20 6669 782e 0a0a 1f0a 4669 6c65 to fix.....File\n+00017f50: 3a20 736b 6574 6368 2e69 6e66 6f2c 2020 : sketch.info, \n+00017f60: 4e6f 6465 3a20 4c69 6d69 7473 206f 6e20 Node: Limits on \n+00017f70: 6572 726f 7220 6465 7465 6374 696f 6e2c error detection,\n+00017f80: 2020 4e65 7874 3a20 436c 6970 7069 6e67 Next: Clipping\n+00017f90: 2c20 2050 7265 763a 2043 6176 6561 7473 , Prev: Caveats\n+00017fa0: 2c20 2055 703a 2043 6176 6561 7473 0a0a , Up: Caveats..\n+00017fb0: 342e 342e 3120 4c69 6d69 7473 206f 6e20 4.4.1 Limits on \n+00017fc0: e280 9873 6b65 7463 68e2 8099 2065 7272 ...sketch... err\n+00017fd0: 6f72 2064 6574 6563 7469 6f6e 0a2d 2d2d or detection.---\n 00017fe0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00017ff0: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00018000: 2d2d 2d2d 2d2d 2d0a 0ae2 8098 536b 6574 -------.....Sket\n-00018010: 6368 e280 9920 6361 7463 6865 7320 6d61 ch... catches ma\n-00018020: 6e79 206b 696e 6473 206f 6620 6572 726f ny kinds of erro\n-00018030: 7273 2c20 6275 7420 6e6f 7420 616c 6c2e rs, but not all.\n-00018040: 2020 466f 7220 6578 616d 706c 652c 0a6f For example,.o\n-00018050: 7074 696f 6e73 2074 6861 7420 736b 6574 ptions that sket\n-00018060: 6368 2064 6f65 7320 6e6f 7420 7265 636f ch does not reco\n-00018070: 676e 697a 652c 2065 7665 6e20 696e 636f gnize, even inco\n-00018080: 7272 6563 7420 6f6e 6573 2c20 6172 6520 rrect ones, are \n-00018090: 7175 6965 746c 790a 636f 7069 6564 2074 quietly.copied t\n-000180a0: 6f20 e280 9850 5354 7269 636b 73e2 8099 o ...PSTricks...\n-000180b0: 2063 6f6d 6d61 6e64 7320 696e 2074 6865 commands in the\n-000180c0: 206f 7574 7075 742e 2020 4974 2069 7320 output. It is \n-000180d0: 616c 736f 2075 6e66 6f72 7475 6e61 7465 also unfortunate\n-000180e0: 6c79 0a65 6173 7920 746f 2070 726f 6475 ly.easy to produ\n-000180f0: 6365 20e2 8098 736b 6574 6368 e280 9920 ce ...sketch... \n-00018100: 696e 7075 7473 2074 6861 7420 6c65 6164 inputs that lead\n-00018110: 2074 6f20 6e6f 2070 6963 7475 7265 2061 to no picture a\n-00018120: 7420 616c 6c20 2869 6d70 726f 7065 720a t all (improper.\n-00018130: 7665 7274 6578 206f 7264 6572 696e 6720 vertex ordering \n-00018140: 6361 7573 6573 2065 7665 7279 7468 696e causes everythin\n-00018150: 6720 746f 2062 6520 6375 6c6c 6564 292c g to be culled),\n-00018160: 2074 6f20 7069 6374 7572 6573 2074 6861 to pictures tha\n-00018170: 7420 6172 650a 746f 6f20 6269 6720 6f72 t are.too big or\n-00018180: 2074 6f6f 2073 6d61 6c6c 2066 6f72 20e2 too small for .\n-00018190: 8098 5053 5472 6963 6b73 e280 9920 746f ..PSTricks... to\n-000181a0: 2064 7261 7720 2864 7565 2074 6f20 6c69 draw (due to li\n-000181b0: 6d69 7473 206f 6620 5465 5820 6d61 7468 mits of TeX math\n-000181c0: 292c 0a61 6e64 2070 6963 7475 7265 7320 ),.and pictures \n-000181d0: 7468 6174 206c 6f6f 6b20 6e6f 7468 696e that look nothin\n-000181e0: 6720 6c69 6b65 2077 6861 7420 7761 7320 g like what was \n-000181f0: 696e 7465 6e64 6564 2e20 2041 2070 6963 intended. 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Always m\n-000182d0: 6169 6e74 6169 6e20 6f6e 6520 6f72 2074 aintain one or t\n-000182e0: 776f 2062 6163 6b2d 7665 7273 696f 6e73 wo back-versions\n-000182f0: 206f 6620 6120 6472 6177 696e 6720 736f of a drawing so\n-00018300: 2074 6861 7420 6974 2069 730a 2020 2020 that it is. \n-00018310: 2065 6173 7920 746f 2066 616c 6c20 6261 easy to fall ba\n-00018320: 636b 2074 6f20 6120 6b6e 6f77 6e2d 676f ck to a known-go\n-00018330: 6f64 2069 6e63 7265 6d65 6e74 2e0a 2020 od increment.. \n-00018340: 20e2 80a2 2057 6865 6e20 7573 696e 6720 ... 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Temporarily us\n-000183f0: 6520 e280 9863 756c 6c3d 6661 6c73 65e2 e ...cull=false.\n-00018400: 8099 2074 6f20 7365 6520 7768 6572 6520 .. to see where \n-00018410: 7665 7274 6578 206f 7264 6572 696e 6720 vertex ordering \n-00018420: 7072 6f62 6c65 6d73 0a20 2020 2020 6c69 problems. li\n-00018430: 652e 0a20 2020 e280 a220 5573 6520 7465 e.. ... 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T\n-000185f0: 6865 2065 6e74 6972 650a 7363 656e 6520 he entire.scene \n-00018600: 6973 2061 6c77 6179 7320 6472 6177 6e2e is always drawn.\n-00018610: 2020 5468 6973 206d 6561 6e73 2074 6861 This means tha\n-00018620: 7420 7768 656e 2061 2070 6572 7370 6563 t when a perspec\n-00018630: 7469 7665 2074 7261 6e73 666f 726d 2069 tive transform i\n-00018640: 730a 656d 706c 6f79 6564 2c20 6974 2069 s.employed, it i\n-00018650: 7320 7468 6520 7573 6572 2773 2072 6573 s the user's res\n-00018660: 706f 6e73 6962 696c 6974 7920 746f 206d ponsibility to m\n-00018670: 616b 6520 7375 7265 2074 6865 2065 6e74 ake sure the ent\n-00018680: 6972 6520 7363 656e 650a 7265 6d61 696e ire scene.remain\n-00018690: 7320 696e 2066 726f 6e74 206f 6620 7468 s in front of th\n-000186a0: 6520 7669 6577 6572 2c20 7468 6520 7265 e viewer, the re\n-000186b0: 6769 6f6e 207a 3c30 2e0a 0a1f 0a46 696c gion z<0.....Fil\n-000186c0: 653a 2073 6b65 7463 682e 696e 666f 2c20 e: sketch.info, \n-000186d0: 204e 6f64 653a 2048 6964 6465 6e20 7375 Node: Hidden su\n-000186e0: 7266 6163 6520 7265 6d6f 7661 6c2c 2020 rface removal, \n-000186f0: 5072 6576 3a20 436c 6970 7069 6e67 2c20 Prev: Clipping, \n-00018700: 2055 703a 2043 6176 6561 7473 0a0a 342e Up: Caveats..4.\n-00018710: 342e 3320 4869 6464 656e 2073 7572 6661 4.3 Hidden surfa\n-00018720: 6365 2072 656d 6f76 616c 2061 6e64 2070 ce removal and p\n-00018730: 6f6c 7967 6f6e 2073 706c 6974 7469 6e67 olygon splitting\n-00018740: 0a2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d .---------------\n+00018000: 2d2d 2d2d 2d0a 0ae2 8098 536b 6574 6368 -----.....Sketch\n+00018010: e280 9920 6361 7463 6865 7320 6d61 6e79 ... catches many\n+00018020: 206b 696e 6473 206f 6620 6572 726f 7273 kinds of errors\n+00018030: 2c20 6275 7420 6e6f 7420 616c 6c2e 2020 , but not all. \n+00018040: 466f 7220 6578 616d 706c 652c 0a6f 7074 For example,.opt\n+00018050: 696f 6e73 2074 6861 7420 736b 6574 6368 ions that sketch\n+00018060: 2064 6f65 7320 6e6f 7420 7265 636f 676e does not recogn\n+00018070: 697a 652c 2065 7665 6e20 696e 636f 7272 ize, even incorr\n+00018080: 6563 7420 6f6e 6573 2c20 6172 6520 7175 ect ones, are qu\n+00018090: 6965 746c 790a 636f 7069 6564 2074 6f20 ietly.copied to \n+000180a0: e280 9850 5354 7269 636b 73e2 8099 2063 ...PSTricks... c\n+000180b0: 6f6d 6d61 6e64 7320 696e 2074 6865 206f ommands in the o\n+000180c0: 7574 7075 742e 2020 4974 2069 7320 616c utput. It is al\n+000180d0: 736f 2075 6e66 6f72 7475 6e61 7465 6c79 so unfortunately\n+000180e0: 0a65 6173 7920 746f 2070 726f 6475 6365 .easy to produce\n+000180f0: 20e2 8098 736b 6574 6368 e280 9920 696e ...sketch... in\n+00018100: 7075 7473 2074 6861 7420 6c65 6164 2074 puts that lead t\n+00018110: 6f20 6e6f 2070 6963 7475 7265 2061 7420 o no picture at \n+00018120: 616c 6c20 2869 6d70 726f 7065 720a 7665 all (improper.ve\n+00018130: 7274 6578 206f 7264 6572 696e 6720 6361 rtex ordering ca\n+00018140: 7573 6573 2065 7665 7279 7468 696e 6720 uses everything \n+00018150: 746f 2062 6520 6375 6c6c 6564 292c 2074 to be culled), t\n+00018160: 6f20 7069 6374 7572 6573 2074 6861 7420 o pictures that \n+00018170: 6172 650a 746f 6f20 6269 6720 6f72 2074 are.too big or t\n+00018180: 6f6f 2073 6d61 6c6c 2066 6f72 20e2 8098 oo small for ...\n+00018190: 5053 5472 6963 6b73 e280 9920 746f 2064 PSTricks... to d\n+000181a0: 7261 7720 2864 7565 2074 6f20 6c69 6d69 raw (due to limi\n+000181b0: 7473 206f 6620 5465 5820 6d61 7468 292c ts of TeX math),\n+000181c0: 0a61 6e64 2070 6963 7475 7265 7320 7468 .and pictures th\n+000181d0: 6174 206c 6f6f 6b20 6e6f 7468 696e 6720 at look nothing \n+000181e0: 6c69 6b65 2077 6861 7420 7761 7320 696e like what was in\n+000181f0: 7465 6e64 6564 2e20 2041 2070 6963 7475 tended. A pictu\n+00018200: 7265 2077 6974 680a 6f6e 6520 6f66 2074 re with.one of t\n+00018210: 6865 7365 2070 726f 626c 656d 7320 6361 hese problems ca\n+00018220: 6e20 6265 2064 6966 6669 6375 6c74 2074 n be difficult t\n+00018230: 6f20 2264 6562 7567 2e22 2020 5765 206f o \"debug.\" We o\n+00018240: 6666 6572 2074 6865 0a66 6f6c 6c6f 7769 ffer the.followi\n+00018250: 6e67 2073 7567 6765 7374 696f 6e73 2e0a ng suggestions..\n+00018260: 2020 20e2 80a2 2046 6f6c 6c6f 7720 7468 ... Follow th\n+00018270: 6520 7375 6767 6573 7465 6420 696e 6372 e suggested incr\n+00018280: 656d 656e 7461 6c20 6465 7665 6c6f 706d emental developm\n+00018290: 656e 7420 6d65 7468 6f64 2064 6573 6372 ent method descr\n+000182a0: 6962 6564 2069 6e0a 2020 2020 202a 6e6f ibed in. *no\n+000182b0: 7465 204f 7665 7276 6965 773a 3a2e 0a20 te Overview::.. \n+000182c0: 2020 e280 a220 416c 7761 7973 206d 6169 ... Always mai\n+000182d0: 6e74 6169 6e20 6f6e 6520 6f72 2074 776f ntain one or two\n+000182e0: 2062 6163 6b2d 7665 7273 696f 6e73 206f back-versions o\n+000182f0: 6620 6120 6472 6177 696e 6720 736f 2074 f a drawing so t\n+00018300: 6861 7420 6974 2069 730a 2020 2020 2065 hat it is. e\n+00018310: 6173 7920 746f 2066 616c 6c20 6261 636b asy to fall back\n+00018320: 2074 6f20 6120 6b6e 6f77 6e2d 676f 6f64 to a known-good\n+00018330: 2069 6e63 7265 6d65 6e74 2e0a 2020 20e2 increment.. .\n+00018340: 80a2 2057 6865 6e20 7573 696e 6720 e280 .. 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Use temp\n+00018440: 6f72 6172 7920 6368 616e 6765 7320 6f66 orary changes of\n+00018450: 2063 6f6c 6f72 206f 6620 6f6e 6520 6f72 color of one or\n+00018460: 206d 6f72 6520 6f62 6a65 6374 7320 746f more objects to\n+00018470: 2065 6e73 7572 650a 2020 2020 2074 6861 ensure. tha\n+00018480: 7420 796f 7572 2075 6e64 6572 7374 616e t your understan\n+00018490: 6469 6e67 206f 6620 7468 6520 7363 656e ding of the scen\n+000184a0: 6520 6765 6f6d 6574 7279 2069 7320 636f e geometry is co\n+000184b0: 7272 6563 742e 0a20 2020 e280 a220 4966 rrect.. ... If\n+000184c0: 20e2 8098 5053 5472 6963 6b73 e280 9920 ...PSTricks... \n+000184d0: 636f 6d70 6c61 696e 7320 6162 6f75 7420 complains about \n+000184e0: 736f 6d65 7468 696e 672c 2069 6e73 7065 something, inspe\n+000184f0: 6374 2074 6865 206f 7574 7075 740a 2020 ct the output. \n+00018500: 2020 2064 6972 6563 746c 7920 666f 7220 directly for \n+00018510: 636c 7565 732e 0a0a 1f0a 4669 6c65 3a20 clues.....File: \n+00018520: 736b 6574 6368 2e69 6e66 6f2c 2020 4e6f sketch.info, No\n+00018530: 6465 3a20 436c 6970 7069 6e67 2c20 204e de: Clipping, N\n+00018540: 6578 743a 2048 6964 6465 6e20 7375 7266 ext: Hidden surf\n+00018550: 6163 6520 7265 6d6f 7661 6c2c 2020 5072 ace removal, Pr\n+00018560: 6576 3a20 4c69 6d69 7473 206f 6e20 6572 ev: Limits on er\n+00018570: 726f 7220 6465 7465 6374 696f 6e2c 2020 ror detection, \n+00018580: 5570 3a20 4361 7665 6174 730a 0a34 2e34 Up: Caveats..4.4\n+00018590: 2e32 2043 6c69 7070 696e 670a 2d2d 2d2d .2 Clipping.----\n+000185a0: 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a 5468 6520 ----------..The \n+000185b0: 6375 7272 656e 7420 7665 7273 696f 6e20 current version \n+000185c0: 6f66 20e2 8098 736b 6574 6368 e280 9920 of ...sketch... \n+000185d0: 6861 7320 6e6f 2063 6c69 7070 696e 6720 has no clipping \n+000185e0: 6f70 6572 6174 696f 6e73 2e20 2054 6865 operations. The\n+000185f0: 2065 6e74 6972 650a 7363 656e 6520 6973 entire.scene is\n+00018600: 2061 6c77 6179 7320 6472 6177 6e2e 2020 always drawn. \n+00018610: 5468 6973 206d 6561 6e73 2074 6861 7420 This means that \n+00018620: 7768 656e 2061 2070 6572 7370 6563 7469 when a perspecti\n+00018630: 7665 2074 7261 6e73 666f 726d 2069 730a ve transform is.\n+00018640: 656d 706c 6f79 6564 2c20 6974 2069 7320 employed, it is \n+00018650: 7468 6520 7573 6572 2773 2072 6573 706f the user's respo\n+00018660: 6e73 6962 696c 6974 7920 746f 206d 616b nsibility to mak\n+00018670: 6520 7375 7265 2074 6865 2065 6e74 6972 e sure the entir\n+00018680: 6520 7363 656e 650a 7265 6d61 696e 7320 e scene.remains \n+00018690: 696e 2066 726f 6e74 206f 6620 7468 6520 in front of the \n+000186a0: 7669 6577 6572 2c20 7468 6520 7265 6769 viewer, the regi\n+000186b0: 6f6e 207a 3c30 2e0a 0a1f 0a46 696c 653a on z<0.....File:\n+000186c0: 2073 6b65 7463 682e 696e 666f 2c20 204e sketch.info, N\n+000186d0: 6f64 653a 2048 6964 6465 6e20 7375 7266 ode: Hidden surf\n+000186e0: 6163 6520 7265 6d6f 7661 6c2c 2020 5072 ace removal, Pr\n+000186f0: 6576 3a20 436c 6970 7069 6e67 2c20 2055 ev: Clipping, U\n+00018700: 703a 2043 6176 6561 7473 0a0a 342e 342e p: Caveats..4.4.\n+00018710: 3320 4869 6464 656e 2073 7572 6661 6365 3 Hidden surface\n+00018720: 2072 656d 6f76 616c 2061 6e64 2070 6f6c removal and pol\n+00018730: 7967 6f6e 2073 706c 6974 7469 6e67 0a2d ygon splitting.-\n+00018740: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00018750: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n 00018760: 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d 2d2d ----------------\n-00018770: 2d2d 2d0a 0ae2 8098 536b 6574 6368 e280 ---.....Sketch..\n-00018780: 9920 7573 6573 2074 6865 20e2 809c 6465 . uses the ...de\n-00018790: 7074 6820 736f 7274 2061 6c67 6f72 6974 pth sort algorit\n-000187a0: 686d e280 9d20 666f 7220 6869 6464 656e hm... for hidden\n-000187b0: 2073 7572 6661 6365 2072 656d 6f76 616c surface removal\n-000187c0: 2e0a 5468 6973 2069 7320 6120 7665 7279 ..This is a very\n-000187d0: 206f 6c64 2074 6563 686e 6971 7565 2064 old technique d\n-000187e0: 7565 2074 6f20 4e65 7765 6c6c 2e28 3129 ue to Newell.(1)\n-000187f0: 2020 4974 2069 7320 6765 6e65 7261 6c6c It is generall\n-00018800: 7920 7265 6761 7264 6564 0a61 7320 746f y regarded.as to\n-00018810: 6f20 736c 6f77 2066 6f72 2072 6561 6c20 o slow for real \n-00018820: 7469 6d65 2067 7261 7068 6963 732c 2062 time graphics, b\n-00018830: 7574 2069 7420 6973 2069 6465 616c 2066 ut it is ideal f\n-00018840: 6f72 206f 7572 2070 7572 706f 7365 0a77 or our purpose.w\n-00018850: 6865 7265 2073 7065 6564 2069 7320 6e6f here speed is no\n-00018860: 7420 7665 7279 2069 6d70 6f72 7461 6e74 t very important\n-00018870: 2e28 3229 0a0a 2020 2054 6865 2064 6570 .(2).. The dep\n-00018880: 7468 2073 6f72 7420 616c 676f 7269 7468 th sort algorith\n-00018890: 6d20 6d65 7265 6c79 2073 6f72 7473 206f m merely sorts o\n-000188a0: 626a 6563 7473 206f 6e20 6120 6b65 7920 bjects on a key \n-000188b0: 6f66 2069 6e63 7265 6173 696e 670a 7a2d of increasing.z-\n-000188c0: 636f 6f72 6469 6e61 7465 2c20 6571 7569 coordinate, equi\n-000188d0: 7661 6c65 6e74 2074 6f20 6465 6372 6561 valent to decrea\n-000188e0: 7369 6e67 2064 6570 7468 2e20 204f 626a sing depth. Obj\n-000188f0: 6563 7473 2061 7265 2074 6865 6e20 6472 ects are then dr\n-00018900: 6177 6e20 696e 0a74 6865 2073 6f72 7465 awn in.the sorte\n-00018910: 6420 7365 7175 656e 6365 2073 6f20 7468 d sequence so th\n-00018920: 6174 2074 686f 7365 2061 7420 7468 6520 at those at the \n-00018930: 7265 6172 206f 6620 7468 6520 7363 656e rear of the scen\n-00018940: 6520 6172 650a 6f76 6572 7772 6974 7465 e are.overwritte\n-00018950: 6e20 6279 2074 686f 7365 2063 6c6f 7365 n by those close\n-00018960: 7220 746f 2074 6865 2076 6965 7765 722e r to the viewer.\n-00018970: 2020 5369 6e63 6520 7468 6973 2069 7320 Since this is \n-00018980: 616c 736f 2068 6f77 206f 696c 0a70 6169 also how oil.pai\n-00018990: 6e74 6572 7320 7072 6163 7469 6365 2074 nters practice t\n-000189a0: 6865 6972 2061 7274 2c20 6465 7074 6820 heir art, depth \n-000189b0: 736f 7274 2069 7320 736f 6d65 7469 6d65 sort is sometime\n-000189c0: 7320 6361 6c6c 6564 2022 7468 650a 7061 s called \"the.pa\n-000189d0: 696e 7465 7227 7320 616c 676f 7269 7468 inter's algorith\n-000189e0: 6d2e 220a 0a20 2020 496e 2073 6f6d 6520 m.\".. In some \n-000189f0: 6361 7365 7320 6974 2069 7320 696d 706f cases it is impo\n-00018a00: 7373 6962 6c65 2074 6f20 7374 7269 6374 ssible to strict\n-00018a10: 6c79 206f 7264 6572 2070 6f6c 7967 6f6e ly order polygon\n-00018a20: 7320 6163 636f 7264 696e 670a 746f 2064 s according.to d\n-00018a30: 6570 7468 2e20 204d 6f72 656f 7665 722c epth. Moreover,\n-00018a40: 2065 7665 6e20 6966 2061 2063 6f72 7265 even if a corre\n-00018a50: 6374 2064 6570 7468 206f 7264 6572 696e ct depth orderin\n-00018a60: 6720 6578 6973 7473 2c20 7468 650a 636f g exists, the.co\n-00018a70: 6d70 7574 6174 696f 6e20 6e65 6564 6564 mputation needed\n-00018a80: 2074 6f20 6669 6e64 2069 7420 6d61 7920 to find it may \n-00018a90: 6265 2074 6f6f 2063 6f6d 706c 6578 2061 be too complex a\n-00018aa0: 6e64 2073 6c6f 772e 2020 496e 2074 6865 nd slow. In the\n-00018ab0: 7365 0a63 6173 6573 2c20 e280 9873 6b65 se.cases, ...ske\n-00018ac0: 7463 68e2 8099 2073 706c 6974 7320 6f6e tch... splits on\n-00018ad0: 6520 6f72 206d 6f72 6520 706f 6c79 676f e or more polygo\n-00018ae0: 6e73 2069 6e74 6f20 7069 6563 6573 2e20 ns into pieces. \n-00018af0: 2054 6865 0a65 7870 6563 7461 7469 6f6e The.expectation\n-00018b00: 2069 7320 7468 6174 2074 6865 206e 6577 is that the new\n-00018b10: 2c20 736d 616c 6c65 7220 706f 6c79 676f , smaller polygo\n-00018b20: 6e73 2077 696c 6c20 6265 2073 696d 706c ns will be simpl\n-00018b30: 6572 2074 6f20 6f72 6465 722e 0ae2 8098 er to order.....\n-00018b40: 536b 6574 6368 e280 9920 7573 6573 2061 Sketch... uses a\n-00018b50: 2042 5350 2028 6269 6e61 7279 2073 7061 BSP (binary spa\n-00018b60: 6365 2070 6172 7469 7469 6f6e 2920 746f ce partition) to\n-00018b70: 2068 616e 646c 6520 7468 6520 7370 6c69 handle the spli\n-00018b80: 7474 696e 670a 6f70 6572 6174 696f 6e2e tting.operation.\n-00018b90: 0a0a 2a20 4d65 6e75 3a0a 0a2a 2053 7461 ..* Menu:..* Sta\n-00018ba0: 7469 7374 6963 733a 3a20 2020 2020 2020 tistics:: \n-00018bb0: 2020 2020 2020 2020 2020 2050 6572 666f Perfo\n-00018bc0: 726d 616e 6365 206e 756d 6265 7273 206f rmance numbers o\n-00018bd0: 6e20 6465 7074 6820 736f 7274 2e0a 2a20 n depth sort..* \n-00018be0: 4275 6773 2061 6e64 2061 6e6f 6d61 6c69 Bugs and anomali\n-00018bf0: 6573 3a3a 2020 2020 2020 2020 2020 496d es:: Im\n-00018c00: 7065 7266 6563 7469 6f6e 7320 696e 2074 perfections in t\n-00018c10: 6869 7320 696d 706c 656d 656e 7461 7469 his implementati\n-00018c20: 6f6e 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d on... --------\n-00018c30: 2d2d 2046 6f6f 746e 6f74 6573 202d 2d2d -- Footnotes ---\n-00018c40: 2d2d 2d2d 2d2d 2d0a 0a20 2020 2831 2920 -------.. (1) \n-00018c50: 4e65 7765 6c6c 2c20 4d2e 452e 2c20 522e Newell, M.E., R.\n-00018c60: 472e 204e 6577 656c 6c2c 2061 6e64 2054 G. Newell, and T\n-00018c70: 2e4c 2e20 5361 6e63 6861 2c20 4120 736f .L. Sancha, A so\n-00018c80: 6c75 7469 6f6e 2074 6f20 7468 650a 6869 lution to the.hi\n-00018c90: 6464 656e 2073 7572 6661 6365 2070 726f dden surface pro\n-00018ca0: 626c 656d 2e20 2050 726f 6365 6564 696e blem. Proceedin\n-00018cb0: 6773 206f 6620 7468 6520 4143 4d20 616e gs of the ACM an\n-00018cc0: 6e75 616c 2063 6f6e 6665 7265 6e63 6520 nual conference \n-00018cd0: 2d0a 566f 6c75 6d65 2031 2c20 7061 6765 -.Volume 1, page\n-00018ce0: 2034 3433 2d34 3530 2c20 4143 4d20 5072 443-450, ACM Pr\n-00018cf0: 6573 732c 2031 3937 322e 0a0a 2020 2028 ess, 1972... (\n-00018d00: 3229 2057 6520 6861 7665 2072 756e 20e2 2) We have run .\n-00018d10: 8098 736b 6574 6368 e280 9920 6f6e 2074 ..sketch... on t\n-00018d20: 6865 2066 616d 6f75 7320 5374 616e 666f he famous Stanfo\n-00018d30: 7264 2042 756e 6e79 2c20 7768 6963 6820 rd Bunny, which \n-00018d40: 636f 6e73 6973 7473 0a6f 6620 6e65 6172 consists.of near\n-00018d50: 6c79 2037 302c 3030 3020 7472 6961 6e67 ly 70,000 triang\n-00018d60: 6c65 732e 2020 5275 6e20 7469 6d65 2077 les. Run time w\n-00018d70: 6173 2061 626f 7574 2036 2073 6563 6f6e as about 6 secon\n-00018d80: 6473 2e20 204d 6f73 7420 6f66 2074 6869 ds. Most of thi\n-00018d90: 730a 7761 7320 7370 656e 7420 7772 6974 s.was spent writ\n-00018da0: 696e 6720 7468 6520 6f75 7470 7574 2066 ing the output f\n-00018db0: 696c 6520 7261 7468 6572 2074 6861 6e20 ile rather than \n-00018dc0: 696e 2074 6865 2068 6964 6465 6e20 7375 in the hidden su\n-00018dd0: 7266 6163 650a 616c 676f 7269 7468 6d2e rface.algorithm.\n-00018de0: 2020 4c61 5465 5820 746f 6f6b 206d 7563 LaTeX took muc\n-00018df0: 6820 6c6f 6e67 6572 2074 6f20 7072 6f63 h longer to proc\n-00018e00: 6573 7320 7468 6520 7265 7375 6c74 696e ess the resultin\n-00018e10: 6720 e280 9850 5354 7269 636b 73e2 8099 g ...PSTricks...\n-00018e20: 0a63 6f64 652e 2020 5468 6520 6f62 7669 .code. The obvi\n-00018e30: 6f75 7320 636f 6e63 6c75 7369 6f6e 2069 ous conclusion i\n-00018e40: 7320 7468 6174 2074 6865 2073 7065 6564 s that the speed\n-00018e50: 206f 6620 7468 6520 6465 7074 6820 736f of the depth so\n-00018e60: 7274 0a61 6c67 6f72 6974 686d 2069 7320 rt.algorithm is \n-00018e70: 6e6f 7420 6120 776f 7272 792e 0a0a 1f0a not a worry.....\n-00018e80: 4669 6c65 3a20 736b 6574 6368 2e69 6e66 File: sketch.inf\n-00018e90: 6f2c 2020 4e6f 6465 3a20 5374 6174 6973 o, Node: Statis\n-00018ea0: 7469 6373 2c20 204e 6578 743a 2042 7567 tics, Next: Bug\n-00018eb0: 7320 616e 6420 616e 6f6d 616c 6965 732c s and anomalies,\n-00018ec0: 2020 5072 6576 3a20 4869 6464 656e 2073 Prev: Hidden s\n-00018ed0: 7572 6661 6365 2072 656d 6f76 616c 2c20 urface removal, \n-00018ee0: 2055 703a 2048 6964 6465 6e20 7375 7266 Up: Hidden surf\n-00018ef0: 6163 6520 7265 6d6f 7661 6c0a 0a34 2e34 ace removal..4.4\n-00018f00: 2e33 2e31 2053 7461 7469 7374 6963 730a .3.1 Statistics.\n+00018770: 2d0a 0ae2 8098 536b 6574 6368 e280 9920 -.....Sketch... \n+00018780: 7573 6573 2074 6865 20e2 809c 6465 7074 uses the ...dept\n+00018790: 6820 736f 7274 2061 6c67 6f72 6974 686d h sort algorithm\n+000187a0: e280 9d20 666f 7220 6869 6464 656e 2073 ... for hidden s\n+000187b0: 7572 6661 6365 2072 656d 6f76 616c 2e0a urface removal..\n+000187c0: 5468 6973 2069 7320 6120 7665 7279 206f This is a very o\n+000187d0: 6c64 2074 6563 686e 6971 7565 2064 7565 ld technique due\n+000187e0: 2074 6f20 4e65 7765 6c6c 2e28 3129 2020 to Newell.(1) \n+000187f0: 4974 2069 7320 6765 6e65 7261 6c6c 7920 It is generally \n+00018800: 7265 6761 7264 6564 0a61 7320 746f 6f20 regarded.as too \n+00018810: 736c 6f77 2066 6f72 2072 6561 6c20 7469 slow for real ti\n+00018820: 6d65 2067 7261 7068 6963 732c 2062 7574 me graphics, but\n+00018830: 2069 7420 6973 2069 6465 616c 2066 6f72 it is ideal for\n+00018840: 206f 7572 2070 7572 706f 7365 0a77 6865 our purpose.whe\n+00018850: 7265 2073 7065 6564 2069 7320 6e6f 7420 re speed is not \n+00018860: 7665 7279 2069 6d70 6f72 7461 6e74 2e28 very important.(\n+00018870: 3229 0a0a 2020 2054 6865 2064 6570 7468 2).. The depth\n+00018880: 2073 6f72 7420 616c 676f 7269 7468 6d20 sort algorithm \n+00018890: 6d65 7265 6c79 2073 6f72 7473 206f 626a merely sorts obj\n+000188a0: 6563 7473 206f 6e20 6120 6b65 7920 6f66 ects on a key of\n+000188b0: 2069 6e63 7265 6173 696e 670a 7a2d 636f increasing.z-co\n+000188c0: 6f72 6469 6e61 7465 2c20 6571 7569 7661 ordinate, equiva\n+000188d0: 6c65 6e74 2074 6f20 6465 6372 6561 7369 lent to decreasi\n+000188e0: 6e67 2064 6570 7468 2e20 204f 626a 6563 ng depth. Objec\n+000188f0: 7473 2061 7265 2074 6865 6e20 6472 6177 ts are then draw\n+00018900: 6e20 696e 0a74 6865 2073 6f72 7465 6420 n in.the sorted \n+00018910: 7365 7175 656e 6365 2073 6f20 7468 6174 sequence so that\n+00018920: 2074 686f 7365 2061 7420 7468 6520 7265 those at the re\n+00018930: 6172 206f 6620 7468 6520 7363 656e 6520 ar of the scene \n+00018940: 6172 650a 6f76 6572 7772 6974 7465 6e20 are.overwritten \n+00018950: 6279 2074 686f 7365 2063 6c6f 7365 7220 by those closer \n+00018960: 746f 2074 6865 2076 6965 7765 722e 2020 to the viewer. \n+00018970: 5369 6e63 6520 7468 6973 2069 7320 616c Since this is al\n+00018980: 736f 2068 6f77 206f 696c 0a70 6169 6e74 so how oil.paint\n+00018990: 6572 7320 7072 6163 7469 6365 2074 6865 ers practice the\n+000189a0: 6972 2061 7274 2c20 6465 7074 6820 736f ir art, depth so\n+000189b0: 7274 2069 7320 736f 6d65 7469 6d65 7320 rt is sometimes \n+000189c0: 6361 6c6c 6564 2022 7468 650a 7061 696e called \"the.pain\n+000189d0: 7465 7227 7320 616c 676f 7269 7468 6d2e ter's algorithm.\n+000189e0: 220a 0a20 2020 496e 2073 6f6d 6520 6361 \".. In some ca\n+000189f0: 7365 7320 6974 2069 7320 696d 706f 7373 ses it is imposs\n+00018a00: 6962 6c65 2074 6f20 7374 7269 6374 6c79 ible to strictly\n+00018a10: 206f 7264 6572 2070 6f6c 7967 6f6e 7320 order polygons \n+00018a20: 6163 636f 7264 696e 670a 746f 2064 6570 according.to dep\n+00018a30: 7468 2e20 204d 6f72 656f 7665 722c 2065 th. Moreover, e\n+00018a40: 7665 6e20 6966 2061 2063 6f72 7265 6374 ven if a correct\n+00018a50: 2064 6570 7468 206f 7264 6572 696e 6720 depth ordering \n+00018a60: 6578 6973 7473 2c20 7468 650a 636f 6d70 exists, the.comp\n+00018a70: 7574 6174 696f 6e20 6e65 6564 6564 2074 utation needed t\n+00018a80: 6f20 6669 6e64 2069 7420 6d61 7920 6265 o find it may be\n+00018a90: 2074 6f6f 2063 6f6d 706c 6578 2061 6e64 too complex and\n+00018aa0: 2073 6c6f 772e 2020 496e 2074 6865 7365 slow. In these\n+00018ab0: 0a63 6173 6573 2c20 e280 9873 6b65 7463 .cases, ...sketc\n+00018ac0: 68e2 8099 2073 706c 6974 7320 6f6e 6520 h... splits one \n+00018ad0: 6f72 206d 6f72 6520 706f 6c79 676f 6e73 or more polygons\n+00018ae0: 2069 6e74 6f20 7069 6563 6573 2e20 2054 into pieces. T\n+00018af0: 6865 0a65 7870 6563 7461 7469 6f6e 2069 he.expectation i\n+00018b00: 7320 7468 6174 2074 6865 206e 6577 2c20 s that the new, \n+00018b10: 736d 616c 6c65 7220 706f 6c79 676f 6e73 smaller polygons\n+00018b20: 2077 696c 6c20 6265 2073 696d 706c 6572 will be simpler\n+00018b30: 2074 6f20 6f72 6465 722e 0ae2 8098 536b to order.....Sk\n+00018b40: 6574 6368 e280 9920 7573 6573 2061 2042 etch... uses a B\n+00018b50: 5350 2028 6269 6e61 7279 2073 7061 6365 SP (binary space\n+00018b60: 2070 6172 7469 7469 6f6e 2920 746f 2068 partition) to h\n+00018b70: 616e 646c 6520 7468 6520 7370 6c69 7474 andle the splitt\n+00018b80: 696e 670a 6f70 6572 6174 696f 6e2e 0a0a ing.operation...\n+00018b90: 2a20 4d65 6e75 3a0a 0a2a 2053 7461 7469 * Menu:..* Stati\n+00018ba0: 7374 6963 733a 3a20 2020 2020 2020 2020 stics:: \n+00018bb0: 2020 2020 2020 2020 2050 6572 666f 726d Perform\n+00018bc0: 616e 6365 206e 756d 6265 7273 206f 6e20 ance numbers on \n+00018bd0: 6465 7074 6820 736f 7274 2e0a 2a20 4275 depth sort..* Bu\n+00018be0: 6773 2061 6e64 2061 6e6f 6d61 6c69 6573 gs and anomalies\n+00018bf0: 3a3a 2020 2020 2020 2020 2020 496d 7065 :: Impe\n+00018c00: 7266 6563 7469 6f6e 7320 696e 2074 6869 rfections in thi\n+00018c10: 7320 696d 706c 656d 656e 7461 7469 6f6e s implementation\n+00018c20: 2e0a 0a20 2020 2d2d 2d2d 2d2d 2d2d 2d2d ... ----------\n+00018c30: 2046 6f6f 746e 6f74 6573 202d 2d2d 2d2d Footnotes -----\n+00018c40: 2d2d 2d2d 2d0a 0a20 2020 2831 2920 4e65 -----.. (1) Ne\n+00018c50: 7765 6c6c 2c20 4d2e 452e 2c20 522e 472e well, M.E., R.G.\n+00018c60: 204e 6577 656c 6c2c 2061 6e64 2054 2e4c Newell, and T.L\n+00018c70: 2e20 5361 6e63 6861 2c20 4120 736f 6c75 . Sancha, A solu\n+00018c80: 7469 6f6e 2074 6f20 7468 650a 6869 6464 tion to the.hidd\n+00018c90: 656e 2073 7572 6661 6365 2070 726f 626c en surface probl\n+00018ca0: 656d 2e20 2050 726f 6365 6564 696e 6773 em. Proceedings\n+00018cb0: 206f 6620 7468 6520 4143 4d20 616e 6e75 of the ACM annu\n+00018cc0: 616c 2063 6f6e 6665 7265 6e63 6520 2d0a al conference -.\n+00018cd0: 566f 6c75 6d65 2031 2c20 7061 6765 2034 Volume 1, page 4\n+00018ce0: 3433 2d34 3530 2c20 4143 4d20 5072 6573 43-450, ACM Pres\n+00018cf0: 732c 2031 3937 322e 0a0a 2020 2028 3229 s, 1972... (2)\n+00018d00: 2057 6520 6861 7665 2072 756e 20e2 8098 We have run ...\n+00018d10: 736b 6574 6368 e280 9920 6f6e 2074 6865 sketch... on the\n+00018d20: 2066 616d 6f75 7320 5374 616e 666f 7264 famous Stanford\n+00018d30: 2042 756e 6e79 2c20 7768 6963 6820 636f Bunny, which co\n+00018d40: 6e73 6973 7473 0a6f 6620 6e65 6172 6c79 nsists.of nearly\n+00018d50: 2037 302c 3030 3020 7472 6961 6e67 6c65 70,000 triangle\n+00018d60: 732e 2020 5275 6e20 7469 6d65 2077 6173 s. Run time was\n+00018d70: 2061 626f 7574 2036 2073 6563 6f6e 6473 about 6 seconds\n+00018d80: 2e20 204d 6f73 7420 6f66 2074 6869 730a . Most of this.\n+00018d90: 7761 7320 7370 656e 7420 7772 6974 696e was spent writin\n+00018da0: 6720 7468 6520 6f75 7470 7574 2066 696c g the output fil\n+00018db0: 6520 7261 7468 6572 2074 6861 6e20 696e e rather than in\n+00018dc0: 2074 6865 2068 6964 6465 6e20 7375 7266 the hidden surf\n+00018dd0: 6163 650a 616c 676f 7269 7468 6d2e 2020 ace.algorithm. \n+00018de0: 4c61 5465 5820 746f 6f6b 206d 7563 6820 LaTeX took much \n+00018df0: 6c6f 6e67 6572 2074 6f20 7072 6f63 6573 longer to proces\n+00018e00: 7320 7468 6520 7265 7375 6c74 696e 6720 s the resulting \n+00018e10: e280 9850 5354 7269 636b 73e2 8099 0a63 ...PSTricks....c\n+00018e20: 6f64 652e 2020 5468 6520 6f62 7669 6f75 ode. The obviou\n+00018e30: 7320 636f 6e63 6c75 7369 6f6e 2069 7320 s conclusion is \n+00018e40: 7468 6174 2074 6865 2073 7065 6564 206f that the speed o\n+00018e50: 6620 7468 6520 6465 7074 6820 736f 7274 f the depth sort\n+00018e60: 0a61 6c67 6f72 6974 686d 2069 7320 6e6f .algorithm is no\n+00018e70: 7420 6120 776f 7272 792e 0a0a 1f0a 4669 t a worry.....Fi\n+00018e80: 6c65 3a20 736b 6574 6368 2e69 6e66 6f2c le: sketch.info,\n+00018e90: 2020 4e6f 6465 3a20 5374 6174 6973 7469 Node: Statisti\n+00018ea0: 6373 2c20 204e 6578 743a 2042 7567 7320 cs, Next: Bugs \n+00018eb0: 616e 6420 616e 6f6d 616c 6965 732c 2020 and anomalies, \n+00018ec0: 5072 6576 3a20 4869 6464 656e 2073 7572 Prev: Hidden sur\n+00018ed0: 6661 6365 2072 656d 6f76 616c 2c20 2055 face removal, U\n+00018ee0: 703a 2048 6964 6465 6e20 7375 7266 6163 p: Hidden surfac\n+00018ef0: 6520 7265 6d6f 7661 6c0a 0a34 2e34 2e33 e removal..4.4.3\n+00018f00: 2e31 2053 7461 7469 7374 6963 730a 2e2e .1 Statistics...\n 00018f10: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-00018f20: 2e2e 0a0a 466f 7220 7468 6520 6375 7269 ....For the curi\n-00018f30: 6f75 732c 20e2 8098 736b 6574 6368 e280 ous, ...sketch..\n-00018f40: 9920 7772 6974 6573 206f 6e65 206c 696e . writes one lin\n-00018f50: 6520 6f66 2064 6570 7468 2073 6f72 7420 e of depth sort \n-00018f60: 7374 6174 6973 7469 6373 2e0a 4865 7265 statistics..Here\n-00018f70: 2069 7320 616e 2065 7861 6d70 6c65 2066 is an example f\n-00018f80: 6f72 2061 206c 6172 6765 2063 6f6c 6c65 or a large colle\n-00018f90: 6374 696f 6e20 6f66 2074 7269 616e 676c ction of triangl\n-00018fa0: 6573 2e0a 2020 7265 6d61 726b 2c20 6e6f es.. remark, no\n-00018fb0: 6465 3d33 3438 3234 2070 726f 6265 3d35 de=34824 probe=5\n-00018fc0: 3831 2e39 2073 7761 703d 3520 7370 6c69 81.9 swap=5 spli\n-00018fd0: 743d 3220 2869 6e3d 3420 6f75 743d 3629 t=2 (in=4 out=6)\n-00018fe0: 206f 6c73 3d32 3438 3531 2f30 0a49 7420 ols=24851/0.It \n-00018ff0: 6d65 616e 7320 7468 6174 2033 342c 3832 means that 34,82\n-00019000: 3420 6f62 6a65 6374 7320 7765 7265 2064 4 objects were d\n-00019010: 6570 7468 2073 6f72 7465 6420 6166 7465 epth sorted afte\n-00019020: 7220 6375 6c6c 696e 672e 2020 466f 7220 r culling. For \n-00019030: 6561 6368 2c0a 616e 2061 7665 7261 6765 each,.an average\n-00019040: 206f 6620 3538 312e 3920 6f74 6865 7273 of 581.9 others\n-00019050: 2068 6164 2074 6f20 6265 2063 6865 636b had to be check\n-00019060: 6564 2074 6f20 656e 7375 7265 2074 6861 ed to ensure tha\n-00019070: 7420 7468 6520 696e 6974 6961 6c2c 0a61 t the initial,.a\n-00019080: 7070 726f 7869 6d61 7465 206f 7264 6572 pproximate order\n-00019090: 696e 6720 7761 7320 636f 7272 6563 742e ing was correct.\n-000190a0: 2020 416d 6f6e 6720 616c 6c20 7468 6573 Among all thes\n-000190b0: 6520 6368 6563 6b73 2c20 6f6e 6c79 2035 e checks, only 5\n-000190c0: 0a72 6573 756c 7465 6420 696e 2073 7761 .resulted in swa\n-000190d0: 7073 2074 6f20 7265 6f72 6465 7220 7468 ps to reorder th\n-000190e0: 6520 696e 6974 6961 6c20 736f 7274 2e20 e initial sort. \n-000190f0: 2049 6e20 7477 6f20 6361 7365 732c 2061 In two cases, a\n-00019100: 2063 6f72 7265 6374 0a6f 7264 6572 696e correct.orderin\n-00019110: 6720 636f 756c 6420 6e6f 7420 6265 2064 g could not be d\n-00019120: 6574 6572 6d69 6e65 642c 2073 6f20 6269 etermined, so bi\n-00019130: 6e61 7279 2073 7061 6365 2070 6172 7469 nary space parti\n-00019140: 7469 6f6e 7320 7765 7265 0a63 6f6e 7374 tions were.const\n-00019150: 7275 6374 6564 2066 6f72 2073 706c 6974 ructed for split\n-00019160: 7469 6e67 2e20 2041 2074 6f74 616c 206f ting. A total o\n-00019170: 6620 3420 6f62 6a65 6374 7320 2874 7269 f 4 objects (tri\n-00019180: 616e 676c 6573 2069 6e20 7468 6973 0a63 angles in this.c\n-00019190: 6173 6529 2077 6572 6520 696e 7365 7274 ase) were insert\n-000191a0: 6564 2069 6e20 7468 6520 7061 7274 6974 ed in the partit\n-000191b0: 696f 6e73 2c20 616e 6420 3620 706f 6c79 ions, and 6 poly\n-000191c0: 676f 6e73 2077 6572 6520 7072 6f64 7563 gons were produc\n-000191d0: 6564 2e0a 4669 6e61 6c6c 792c 2032 342c ed..Finally, 24,\n-000191e0: 3835 3120 226c 6173 7420 7265 736f 7274 851 \"last resort\n-000191f0: 2220 706f 6c79 676f 6e20 6f76 6572 6c61 \" polygon overla\n-00019200: 7020 6368 6563 6b73 2077 6572 6520 7065 p checks were pe\n-00019210: 7266 6f72 6d65 640a 6166 7465 7220 7369 rformed.after si\n-00019220: 6d70 6c65 722c 2066 6173 7465 7220 6368 mpler, faster ch\n-00019230: 6563 6b73 2066 6169 6c65 6420 746f 2079 ecks failed to y\n-00019240: 6965 6c64 2063 6f6e 636c 7573 6976 6520 ield conclusive \n-00019250: 7265 7375 6c74 732e 2020 5468 650a 6669 results. The.fi\n-00019260: 6e61 6c20 2f30 2069 7320 666f 7220 6c69 nal /0 is for li\n-00019270: 6e65 2d70 6f6c 7967 6f6e 206f 7665 726c ne-polygon overl\n-00019280: 6170 2063 6865 636b 732e 2020 466f 7220 ap checks. For \n-00019290: 636f 6d70 6172 6973 6f6e 2c20 7468 650a comparison, the.\n-000192a0: 7374 6174 6973 7469 6373 2066 6f72 2074 statistics for t\n-000192b0: 6865 206c 6173 7420 6669 6775 7265 2069 he last figure i\n-000192c0: 6e20 2a6e 6f74 6520 4f76 6572 7669 6577 n *note Overview\n-000192d0: 3a3a 2066 6f6c 6c6f 772e 0a20 2072 656d :: follow.. rem\n-000192e0: 6172 6b2c 206e 6f64 653d 3237 2070 726f ark, node=27 pro\n-000192f0: 6265 3d31 342e 3620 7377 6170 3d33 3620 be=14.6 swap=36 \n-00019300: 7370 6c69 743d 3135 2028 696e 3d33 3020 split=15 (in=30 \n-00019310: 6f75 743d 3435 2920 6f6c 733d 302f 3639 out=45) ols=0/69\n-00019320: 0a4e 6f74 6520 7468 6174 2074 6865 7265 .Note that there\n-00019330: 2077 6173 2070 726f 706f 7274 696f 6e61 was proportiona\n-00019340: 6c6c 7920 6d75 6368 206d 6f72 6520 7377 lly much more sw\n-00019350: 6170 7069 6e67 2061 6e64 2073 706c 6974 apping and split\n-00019360: 7469 6e67 0a61 6374 6976 6974 7920 696e ting.activity in\n-00019370: 2074 6869 7320 6869 6768 6c79 2063 6f6e this highly con\n-00019380: 6e65 6374 6564 2073 6365 6e65 2e0a 0a1f nected scene....\n-00019390: 0a46 696c 653a 2073 6b65 7463 682e 696e .File: sketch.in\n-000193a0: 666f 2c20 204e 6f64 653a 2042 7567 7320 fo, Node: Bugs \n-000193b0: 616e 6420 616e 6f6d 616c 6965 732c 2020 and anomalies, \n-000193c0: 5072 6576 3a20 5374 6174 6973 7469 6373 Prev: Statistics\n-000193d0: 2c20 2055 703a 2048 6964 6465 6e20 7375 , Up: Hidden su\n-000193e0: 7266 6163 6520 7265 6d6f 7661 6c0a 0a34 rface removal..4\n-000193f0: 2e34 2e33 2e32 2042 7567 7320 616e 6420 .4.3.2 Bugs and \n-00019400: 616e 6f6d 616c 6965 730a 2e2e 2e2e 2e2e anomalies.......\n+00018f20: 0a0a 466f 7220 7468 6520 6375 7269 6f75 ..For the curiou\n+00018f30: 732c 20e2 8098 736b 6574 6368 e280 9920 s, ...sketch... \n+00018f40: 7772 6974 6573 206f 6e65 206c 696e 6520 writes one line \n+00018f50: 6f66 2064 6570 7468 2073 6f72 7420 7374 of depth sort st\n+00018f60: 6174 6973 7469 6373 2e0a 4865 7265 2069 atistics..Here i\n+00018f70: 7320 616e 2065 7861 6d70 6c65 2066 6f72 s an example for\n+00018f80: 2061 206c 6172 6765 2063 6f6c 6c65 6374 a large collect\n+00018f90: 696f 6e20 6f66 2074 7269 616e 676c 6573 ion of triangles\n+00018fa0: 2e0a 2020 7265 6d61 726b 2c20 6e6f 6465 .. remark, node\n+00018fb0: 3d33 3438 3234 2070 726f 6265 3d35 3831 =34824 probe=581\n+00018fc0: 2e39 2073 7761 703d 3520 7370 6c69 743d .9 swap=5 split=\n+00018fd0: 3220 2869 6e3d 3420 6f75 743d 3629 206f 2 (in=4 out=6) o\n+00018fe0: 6c73 3d32 3438 3531 2f30 0a49 7420 6d65 ls=24851/0.It me\n+00018ff0: 616e 7320 7468 6174 2033 342c 3832 3420 ans that 34,824 \n+00019000: 6f62 6a65 6374 7320 7765 7265 2064 6570 objects were dep\n+00019010: 7468 2073 6f72 7465 6420 6166 7465 7220 th sorted after \n+00019020: 6375 6c6c 696e 672e 2020 466f 7220 6561 culling. For ea\n+00019030: 6368 2c0a 616e 2061 7665 7261 6765 206f ch,.an average o\n+00019040: 6620 3538 312e 3920 6f74 6865 7273 2068 f 581.9 others h\n+00019050: 6164 2074 6f20 6265 2063 6865 636b 6564 ad to be checked\n+00019060: 2074 6f20 656e 7375 7265 2074 6861 7420 to ensure that \n+00019070: 7468 6520 696e 6974 6961 6c2c 0a61 7070 the initial,.app\n+00019080: 726f 7869 6d61 7465 206f 7264 6572 696e roximate orderin\n+00019090: 6720 7761 7320 636f 7272 6563 742e 2020 g was correct. \n+000190a0: 416d 6f6e 6720 616c 6c20 7468 6573 6520 Among all these \n+000190b0: 6368 6563 6b73 2c20 6f6e 6c79 2035 0a72 checks, only 5.r\n+000190c0: 6573 756c 7465 6420 696e 2073 7761 7073 esulted in swaps\n+000190d0: 2074 6f20 7265 6f72 6465 7220 7468 6520 to reorder the \n+000190e0: 696e 6974 6961 6c20 736f 7274 2e20 2049 initial sort. I\n+000190f0: 6e20 7477 6f20 6361 7365 732c 2061 2063 n two cases, a c\n+00019100: 6f72 7265 6374 0a6f 7264 6572 696e 6720 orrect.ordering \n+00019110: 636f 756c 6420 6e6f 7420 6265 2064 6574 could not be det\n+00019120: 6572 6d69 6e65 642c 2073 6f20 6269 6e61 ermined, so bina\n+00019130: 7279 2073 7061 6365 2070 6172 7469 7469 ry space partiti\n+00019140: 6f6e 7320 7765 7265 0a63 6f6e 7374 7275 ons were.constru\n+00019150: 6374 6564 2066 6f72 2073 706c 6974 7469 cted for splitti\n+00019160: 6e67 2e20 2041 2074 6f74 616c 206f 6620 ng. A total of \n+00019170: 3420 6f62 6a65 6374 7320 2874 7269 616e 4 objects (trian\n+00019180: 676c 6573 2069 6e20 7468 6973 0a63 6173 gles in this.cas\n+00019190: 6529 2077 6572 6520 696e 7365 7274 6564 e) were inserted\n+000191a0: 2069 6e20 7468 6520 7061 7274 6974 696f in the partitio\n+000191b0: 6e73 2c20 616e 6420 3620 706f 6c79 676f ns, and 6 polygo\n+000191c0: 6e73 2077 6572 6520 7072 6f64 7563 6564 ns were produced\n+000191d0: 2e0a 4669 6e61 6c6c 792c 2032 342c 3835 ..Finally, 24,85\n+000191e0: 3120 226c 6173 7420 7265 736f 7274 2220 1 \"last resort\" \n+000191f0: 706f 6c79 676f 6e20 6f76 6572 6c61 7020 polygon overlap \n+00019200: 6368 6563 6b73 2077 6572 6520 7065 7266 checks were perf\n+00019210: 6f72 6d65 640a 6166 7465 7220 7369 6d70 ormed.after simp\n+00019220: 6c65 722c 2066 6173 7465 7220 6368 6563 ler, faster chec\n+00019230: 6b73 2066 6169 6c65 6420 746f 2079 6965 ks failed to yie\n+00019240: 6c64 2063 6f6e 636c 7573 6976 6520 7265 ld conclusive re\n+00019250: 7375 6c74 732e 2020 5468 650a 6669 6e61 sults. The.fina\n+00019260: 6c20 2f30 2069 7320 666f 7220 6c69 6e65 l /0 is for line\n+00019270: 2d70 6f6c 7967 6f6e 206f 7665 726c 6170 -polygon overlap\n+00019280: 2063 6865 636b 732e 2020 466f 7220 636f checks. For co\n+00019290: 6d70 6172 6973 6f6e 2c20 7468 650a 7374 mparison, the.st\n+000192a0: 6174 6973 7469 6373 2066 6f72 2074 6865 atistics for the\n+000192b0: 206c 6173 7420 6669 6775 7265 2069 6e20 last figure in \n+000192c0: 2a6e 6f74 6520 4f76 6572 7669 6577 3a3a *note Overview::\n+000192d0: 2066 6f6c 6c6f 772e 0a20 2072 656d 6172 follow.. remar\n+000192e0: 6b2c 206e 6f64 653d 3237 2070 726f 6265 k, node=27 probe\n+000192f0: 3d31 342e 3620 7377 6170 3d33 3620 7370 =14.6 swap=36 sp\n+00019300: 6c69 743d 3135 2028 696e 3d33 3020 6f75 lit=15 (in=30 ou\n+00019310: 743d 3435 2920 6f6c 733d 302f 3639 0a4e t=45) ols=0/69.N\n+00019320: 6f74 6520 7468 6174 2074 6865 7265 2077 ote that there w\n+00019330: 6173 2070 726f 706f 7274 696f 6e61 6c6c as proportionall\n+00019340: 7920 6d75 6368 206d 6f72 6520 7377 6170 y much more swap\n+00019350: 7069 6e67 2061 6e64 2073 706c 6974 7469 ping and splitti\n+00019360: 6e67 0a61 6374 6976 6974 7920 696e 2074 ng.activity in t\n+00019370: 6869 7320 6869 6768 6c79 2063 6f6e 6e65 his highly conne\n+00019380: 6374 6564 2073 6365 6e65 2e0a 0a1f 0a46 cted scene.....F\n+00019390: 696c 653a 2073 6b65 7463 682e 696e 666f ile: sketch.info\n+000193a0: 2c20 204e 6f64 653a 2042 7567 7320 616e , Node: Bugs an\n+000193b0: 6420 616e 6f6d 616c 6965 732c 2020 5072 d anomalies, Pr\n+000193c0: 6576 3a20 5374 6174 6973 7469 6373 2c20 ev: Statistics, \n+000193d0: 2055 703a 2048 6964 6465 6e20 7375 7266 Up: Hidden surf\n+000193e0: 6163 6520 7265 6d6f 7661 6c0a 0a34 2e34 ace removal..4.4\n+000193f0: 2e33 2e32 2042 7567 7320 616e 6420 616e .3.2 Bugs and an\n+00019400: 6f6d 616c 6965 730a 2e2e 2e2e 2e2e 2e2e omalies.........\n 00019410: 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e 2e2e ................\n-00019420: 2e2e 2e2e 0a0a 506f 6c79 676f 6e20 616e ......Polygon an\n-00019430: 6420 6c69 6e65 2073 706c 6974 7469 6e67 d line splitting\n-00019440: 2063 616e 2062 6f74 6820 6361 7573 6520 can both cause \n-00019450: 616e 6f6d 616c 6965 7320 696e 2074 6865 anomalies in the\n-00019460: 206f 7574 7075 742e 0ae2 8098 5053 5472 output.....PSTr\n-00019470: 6963 6b73 e280 9920 6461 7368 2070 6174 icks... dash pat\n-00019480: 7465 726e 732c 2073 7065 6369 6669 6564 terns, specified\n-00019490: 2077 6974 6820 e280 986c 696e 6573 7479 with ...linesty\n-000194a0: 6c65 3d64 6173 6865 64e2 8099 2c20 6361 le=dashed..., ca\n-000194b0: 6e20 6265 0a64 6973 7275 7074 6564 2062 n be.disrupted b\n-000194c0: 7920 7370 6c69 7474 696e 672e 2020 5468 y splitting. Th\n-000194d0: 6973 206f 6363 7572 7320 7768 656e 2074 is occurs when t\n-000194e0: 6865 2064 6570 7468 2073 6f72 7420 6769 he depth sort gi\n-000194f0: 7665 7320 7570 2074 6f6f 0a65 6172 6c79 ves up too.early\n-00019500: 2061 6e64 2073 706c 6974 7320 6120 6c69 and splits a li\n-00019510: 6e65 2077 6865 7265 2069 7420 6973 206e ne where it is n\n-00019520: 6f74 2072 6561 6c6c 7920 6e65 6365 7373 ot really necess\n-00019530: 6172 792e 2020 4120 776f 726b 6172 6f75 ary. A workarou\n-00019540: 6e64 0a69 7320 746f 2075 7365 2067 7261 nd.is to use gra\n-00019550: 7920 6f72 2066 696e 656c 7920 646f 7474 y or finely dott\n-00019560: 6564 206c 696e 6573 2069 6e73 7465 6164 ed lines instead\n-00019570: 2e20 2049 6620 796f 7572 2064 7261 7769 . If your drawi\n-00019580: 6e67 2069 730a 736d 616c 6c2c 2079 6f75 ng is.small, you\n-00019590: 2063 616e 2061 6c73 6f20 6564 6974 2074 can also edit t\n-000195a0: 6865 20e2 8098 736b 6574 6368 e280 9920 he ...sketch... \n-000195b0: 6f75 7470 7574 2062 7920 6861 6e64 2074 output by hand t\n-000195c0: 6f20 6d65 7267 6520 7468 6520 7069 6563 o merge the piec\n-000195d0: 6573 0a6f 6620 7468 6520 6f66 6665 6e64 es.of the offend\n-000195e0: 696e 6720 6c69 6e65 2e0a 0a20 2020 416e ing line... An\n-000195f0: 6f74 6865 7220 616e 6f6d 616c 7920 6973 other anomaly is\n-00019600: 2074 696e 7920 286f 7220 696e 2064 6567 tiny (or in deg\n-00019610: 656e 6572 6174 6520 6361 7365 7320 6e6f enerate cases no\n-00019620: 742d 736f 2d74 696e 7929 206e 6f74 6368 t-so-tiny) notch\n-00019630: 6573 0a69 6e20 7468 6520 6c69 6e65 7320 es.in the lines \n-00019640: 7468 6174 2062 6f72 6465 7220 7370 6c69 that border spli\n-00019650: 7420 706f 6c79 676f 6e73 2e20 2054 6865 t polygons. The\n-00019660: 7365 2064 6572 6976 6520 6672 6f6d 2074 se derive from t\n-00019670: 6865 2077 6179 2065 6163 680a 706f 6c79 he way each.poly\n-00019680: 676f 6e20 6973 2070 6169 6e74 6564 3a20 gon is painted: \n-00019690: 6669 7273 742c 2061 6c6c 2070 6978 656c first, all pixel\n-000196a0: 7320 7769 7468 696e 2074 6865 2062 6f75 s within the bou\n-000196b0: 6e64 6172 7920 6172 6520 e280 9c66 696c ndary are ...fil\n-000196c0: 6c65 64e2 809d 0a77 6974 6820 636f 6c6f led....with colo\n-000196d0: 7220 2870 6572 6861 7073 2077 6869 7465 r (perhaps white\n-000196e0: 292c 2074 6865 6e20 7468 6520 7361 6d65 ), then the same\n-000196f0: 2062 6f75 6e64 6172 7920 6973 20e2 809c boundary is ...\n-00019700: 7374 726f 6b65 64e2 809d 2028 610a 506f stroked... (a.Po\n-00019710: 7374 7363 7269 7074 2074 6572 6d29 2077 stscript term) w\n-00019720: 6974 6820 6120 6c69 6e65 2e20 2054 6865 ith a line. The\n-00019730: 2072 6573 756c 7420 6973 2074 6861 7420 result is that \n-00019740: 6861 6c66 2074 6865 206c 696e 6520 6c69 half the line li\n-00019750: 6573 0a69 6e73 6964 6520 7468 6520 626f es.inside the bo\n-00019760: 756e 6461 7279 2061 6e64 2068 616c 6620 undary and half \n-00019770: 6f75 7473 6964 652c 2077 6869 6c65 2074 outside, while t\n-00019780: 6865 2050 6169 6e74 6572 2773 2061 6c67 he Painter's alg\n-00019790: 6f72 6974 686d 0a61 7373 756d 6573 2074 orithm.assumes t\n-000197a0: 6865 2070 6f6c 7967 6f6e 206c 6965 7320 he polygon lies \n-000197b0: 656e 7469 7265 6c79 2077 6974 6869 6e20 entirely within \n-000197c0: 6974 7320 626f 756e 6461 7279 2e20 2054 its boundary. 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I\n-00019880: 6e20 6661 6374 20e2 8098 6c69 6e65 7769 n fact ...linewi\n-00019890: 6474 683d 3070 74e2 8099 2069 7320 6775 dth=0pt... is gu\n-000198a0: 6172 616e 7465 6564 2074 6f20 656c 696d aranteed to elim\n-000198b0: 696e 6174 650a 7468 6973 2070 726f 626c inate.this probl\n-000198c0: 656d 2c20 7468 6f75 6768 2074 6869 7320 em, though this \n-000198d0: 7265 7375 6c74 7320 696e 2074 6865 2074 results in the t\n-000198e0: 6869 6e6e 6573 7420 6c69 6e65 2079 6f75 hinnest line you\n-000198f0: 7220 6f75 7470 7574 0a64 6576 6963 6520 r output.device \n-00019900: 6361 6e20 6472 6177 2c20 7768 6963 6820 can draw, which \n-00019910: 6973 2075 7375 616c 6c79 2074 6f6f 2074 is usually too t\n-00019920: 6869 6e2e 2020 596f 7520 6d69 6768 7420 hin. 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Polygon \n-00019a30: 7370 6c69 7474 696e 6720 616c 736f 2062 splitting also b\n-00019a40: 7265 616b 7320 e280 9850 5354 7269 636b reaks ...PSTrick\n-00019a50: 73e2 8099 2068 6174 6368 2070 6174 7465 s... hatch patte\n-00019a60: 726e 732e 2020 5468 6520 6f6e 6c79 0a6b rns. The only.k\n-00019a70: 6e6f 776e 2077 6f72 6b61 726f 756e 6420 nown workaround \n-00019a80: 6973 2074 6f20 7375 6273 7469 7475 7465 is to substitute\n-00019a90: 2061 2073 6f6c 6964 2066 696c 6c20 666f a solid fill fo\n-00019aa0: 7220 7468 6520 6861 7463 682e 0a0a 2020 r the hatch... \n-00019ab0: 202d 2d2d 2d2d 2d2d 2d2d 2d20 466f 6f74 ---------- Foot\n-00019ac0: 6e6f 7465 7320 2d2d 2d2d 2d2d 2d2d 2d2d notes ----------\n-00019ad0: 0a0a 2020 2028 3129 2049 206b 6e6f 7720 .. (1) I know \n-00019ae0: 686f 7720 746f 2066 6978 2074 6869 7320 how to fix this \n-00019af0: 7072 6f62 6c65 6d2c 2062 7574 2049 2064 problem, but I d\n-00019b00: 6f6e 2774 206c 696b 6520 6d79 2073 6f6c on't like my sol\n-00019b10: 7574 696f 6e2c 2061 6e64 0a49 276d 2069 ution, and.I'm i\n-00019b20: 6e74 6572 6573 7465 6420 696e 2079 6f75 nterested in you\n-00019b30: 7273 2e0a 0a1f 0a46 696c 653a 2073 6b65 rs.....File: ske\n-00019b40: 7463 682e 696e 666f 2c20 204e 6f64 653a tch.info, Node:\n-00019b50: 2043 6f6d 6d61 6e64 206c 696e 652c 2020 Command line, \n-00019b60: 4e65 7874 3a20 496e 7374 616c 6c69 6e67 Next: Installing\n-00019b70: 2073 6b65 7463 682c 2020 5072 6576 3a20 sketch, Prev: \n-00019b80: 4275 696c 6469 6e67 2061 2064 7261 7769 Building a drawi\n-00019b90: 6e67 2c20 2055 703a 2054 6f70 0a0a 3520 ng, Up: Top..5 \n-00019ba0: 436f 6d6d 616e 6420 6c69 6e65 0a2a 2a2a Command line.***\n-00019bb0: 2a2a 2a2a 2a2a 2a2a 2a2a 2a0a 0a2a 5379 ***********..*Sy\n-00019bc0: 6e6f 7073 6973 3a2a 0a20 2020 2020 736b nopsis:*. sk\n-00019bd0: 6574 6368 205b 2d68 5d5b 2d56 2078 2e79 etch [-h][-V x.y\n-00019be0: 5d5b 2d76 5d5b 2d62 5d5b 2d64 5d5b 7420 ][-v][-b][-d][t \n-00019bf0: 646f 6374 6d70 5d5b 2d54 5b75 7c65 5d5b doctmp][-T[u|e][\n-00019c00: 705b 507c 545d 5b4c 7c43 5d5d 5d5b 2d6f p[P|T][L|C]]][-o\n-00019c10: 206f 7574 7075 742e 7465 785d 0a20 2020 output.tex]. \n-00019c20: 2020 2020 5b2d 4420 5441 4720 2e2e 2e5d [-D TAG ...]\n-00019c30: 2069 6e70 7574 312e 736b 205b 2d55 2054 input1.sk [-U T\n-00019c40: 4147 202e 2e2e 5d20 696e 7075 7432 2e73 AG ...] input2.s\n-00019c50: 6b20 2e2e 2e0a 0a2a 4465 7363 7269 7074 k .....*Descript\n-00019c60: 696f 6e2a 2050 726f 6365 7373 6573 2074 ion* Processes t\n-00019c70: 6865 20e2 8098 736b 6574 6368 e280 9920 he ...sketch... \n-00019c80: 696e 7075 7420 6669 6c65 7320 696e 206f input files in o\n-00019c90: 7264 6572 2074 6f20 7072 6f64 7563 650a rder to produce.\n-00019ca0: e280 9850 5354 7269 636b 73e2 8099 206f ...PSTricks... o\n-00019cb0: 7574 7075 7420 636f 6465 2073 7569 7461 utput code suita\n-00019cc0: 626c 6520 666f 7220 696e 636c 7573 696f ble for inclusio\n-00019cd0: 6e20 696e 2061 2054 6558 206f 7220 4c61 n in a TeX or La\n-00019ce0: 5465 580a 646f 6375 6d65 6e74 2e0a 0a2a TeX.document...*\n-00019cf0: 4f70 7469 6f6e 733a 2a0a e280 982d 68e2 Options:*....-h.\n-00019d00: 8099 0a20 2020 2020 5072 696e 7420 6120 ... 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A workaround\n+00019540: 0a69 7320 746f 2075 7365 2067 7261 7920 .is to use gray \n+00019550: 6f72 2066 696e 656c 7920 646f 7474 6564 or finely dotted\n+00019560: 206c 696e 6573 2069 6e73 7465 6164 2e20 lines instead. \n+00019570: 2049 6620 796f 7572 2064 7261 7769 6e67 If your drawing\n+00019580: 2069 730a 736d 616c 6c2c 2079 6f75 2063 is.small, you c\n+00019590: 616e 2061 6c73 6f20 6564 6974 2074 6865 an also edit the\n+000195a0: 20e2 8098 736b 6574 6368 e280 9920 6f75 ...sketch... ou\n+000195b0: 7470 7574 2062 7920 6861 6e64 2074 6f20 tput by hand to \n+000195c0: 6d65 7267 6520 7468 6520 7069 6563 6573 merge the pieces\n+000195d0: 0a6f 6620 7468 6520 6f66 6665 6e64 696e .of the offendin\n+000195e0: 6720 6c69 6e65 2e0a 0a20 2020 416e 6f74 g line... Anot\n+000195f0: 6865 7220 616e 6f6d 616c 7920 6973 2074 her anomaly is t\n+00019600: 696e 7920 286f 7220 696e 2064 6567 656e iny (or in degen\n+00019610: 6572 6174 6520 6361 7365 7320 6e6f 742d erate cases not-\n+00019620: 736f 2d74 696e 7929 206e 6f74 6368 6573 so-tiny) notches\n+00019630: 0a69 6e20 7468 6520 6c69 6e65 7320 7468 .in the lines th\n+00019640: 6174 2062 6f72 6465 7220 7370 6c69 7420 at border split \n+00019650: 706f 6c79 676f 6e73 2e20 2054 6865 7365 polygons. These\n+00019660: 2064 6572 6976 6520 6672 6f6d 2074 6865 derive from the\n+00019670: 2077 6179 2065 6163 680a 706f 6c79 676f way each.polygo\n+00019680: 6e20 6973 2070 6169 6e74 6564 3a20 6669 n is painted: fi\n+00019690: 7273 742c 2061 6c6c 2070 6978 656c 7320 rst, all pixels \n+000196a0: 7769 7468 696e 2074 6865 2062 6f75 6e64 within the bound\n+000196b0: 6172 7920 6172 6520 e280 9c66 696c 6c65 ary are ...fille\n+000196c0: 64e2 809d 0a77 6974 6820 636f 6c6f 7220 d....with color \n+000196d0: 2870 6572 6861 7073 2077 6869 7465 292c (perhaps white),\n+000196e0: 2074 6865 6e20 7468 6520 7361 6d65 2062 then the same b\n+000196f0: 6f75 6e64 6172 7920 6973 20e2 809c 7374 oundary is ...st\n+00019700: 726f 6b65 64e2 809d 2028 610a 506f 7374 roked... (a.Post\n+00019710: 7363 7269 7074 2074 6572 6d29 2077 6974 script term) wit\n+00019720: 6820 6120 6c69 6e65 2e20 2054 6865 2072 h a line. The r\n+00019730: 6573 756c 7420 6973 2074 6861 7420 6861 esult is that ha\n+00019740: 6c66 2074 6865 206c 696e 6520 6c69 6573 lf the line lies\n+00019750: 0a69 6e73 6964 6520 7468 6520 626f 756e .inside the boun\n+00019760: 6461 7279 2061 6e64 2068 616c 6620 6f75 dary and half ou\n+00019770: 7473 6964 652c 2077 6869 6c65 2074 6865 tside, while the\n+00019780: 2050 6169 6e74 6572 2773 2061 6c67 6f72 Painter's algor\n+00019790: 6974 686d 0a61 7373 756d 6573 2074 6865 ithm.assumes the\n+000197a0: 2070 6f6c 7967 6f6e 206c 6965 7320 656e polygon lies en\n+000197b0: 7469 7265 6c79 2077 6974 6869 6e20 6974 tirely within it\n+000197c0: 7320 626f 756e 6461 7279 2e20 2054 6865 s boundary. The\n+000197d0: 206e 6f74 6368 6573 2061 7265 0a64 7565 notches are.due\n+000197e0: 2074 6f20 6f6e 6520 706f 6c79 676f 6e20 to one polygon \n+000197f0: 6669 6c6c 206f 7065 7261 7469 6f6e 206f fill operation o\n+00019800: 7665 7277 7269 7469 6e67 2074 6865 2061 verwriting the a\n+00019810: 6c72 6561 6479 2d64 7261 776e 2069 6e73 lready-drawn ins\n+00019820: 6964 650a 6f66 2074 6865 2062 6f72 6465 ide.of the borde\n+00019830: 7220 6f66 2061 6e6f 7468 6572 2070 6f6c r of another pol\n+00019840: 7967 6f6e 2e28 3129 2020 4f6e 6520 776f ygon.(1) One wo\n+00019850: 726b 6172 6f75 6e64 2069 7320 746f 206d rkaround is to m\n+00019860: 616b 6520 626f 7264 6572 0a6c 696e 6573 ake border.lines\n+00019870: 2076 6572 7920 7468 696e 2e20 2049 6e20 very thin. In \n+00019880: 6661 6374 20e2 8098 6c69 6e65 7769 6474 fact ...linewidt\n+00019890: 683d 3070 74e2 8099 2069 7320 6775 6172 h=0pt... is guar\n+000198a0: 616e 7465 6564 2074 6f20 656c 696d 696e anteed to elimin\n+000198b0: 6174 650a 7468 6973 2070 726f 626c 656d ate.this problem\n+000198c0: 2c20 7468 6f75 6768 2074 6869 7320 7265 , though this re\n+000198d0: 7375 6c74 7320 696e 2074 6865 2074 6869 sults in the thi\n+000198e0: 6e6e 6573 7420 6c69 6e65 2079 6f75 7220 nnest line your \n+000198f0: 6f75 7470 7574 0a64 6576 6963 6520 6361 output.device ca\n+00019900: 6e20 6472 6177 2c20 7768 6963 6820 6973 n draw, which is\n+00019910: 2075 7375 616c 6c79 2074 6f6f 2074 6869 usually too thi\n+00019920: 6e2e 2020 596f 7520 6d69 6768 7420 6765 n. You might ge\n+00019930: 7420 6c75 636b 7920 6279 0a6d 6572 656c t lucky by.merel\n+00019940: 7920 7265 6f72 6465 7269 6e67 2074 6869 y reordering thi\n+00019950: 6e67 7320 696e 2074 6865 2069 6e70 7574 ngs in the input\n+00019960: 2066 696c 652c 2077 6869 6368 2069 7320 file, which is \n+00019970: 6c69 6b65 6c79 2074 6f20 6d6f 7665 2074 likely to move t\n+00019980: 6865 0a73 706c 6974 7320 746f 2064 6966 he.splits to dif\n+00019990: 6665 7265 6e74 2070 6c61 6365 732e 2020 ferent places. \n+000199a0: 5468 6520 6f6e 6c79 2073 7572 652d 6669 The only sure-fi\n+000199b0: 7265 2073 6f6c 7574 696f 6e20 6973 2070 re solution is p\n+000199c0: 7265 7474 790a 7465 7272 6962 6c65 3a20 retty.terrible: \n+000199d0: 6375 7374 6f6d 2066 6974 20e2 8098 7370 custom fit ...sp\n+000199e0: 6563 6961 6ce2 8099 206f 7665 726c 6179 ecial... overlay\n+000199f0: 206c 696e 6573 2028 7769 7468 20e2 8098 lines (with ...\n+00019a00: 5c70 736c 696e 65e2 8099 2920 746f 2063 \\psline...) to c\n+00019a10: 6f76 6572 0a74 6865 206e 6f74 6368 6573 over.the notches\n+00019a20: 2e0a 0a20 2020 506f 6c79 676f 6e20 7370 ... Polygon sp\n+00019a30: 6c69 7474 696e 6720 616c 736f 2062 7265 litting also bre\n+00019a40: 616b 7320 e280 9850 5354 7269 636b 73e2 aks ...PSTricks.\n+00019a50: 8099 2068 6174 6368 2070 6174 7465 726e .. hatch pattern\n+00019a60: 732e 2020 5468 6520 6f6e 6c79 0a6b 6e6f s. The only.kno\n+00019a70: 776e 2077 6f72 6b61 726f 756e 6420 6973 wn workaround is\n+00019a80: 2074 6f20 7375 6273 7469 7475 7465 2061 to substitute a\n+00019a90: 2073 6f6c 6964 2066 696c 6c20 666f 7220 solid fill for \n+00019aa0: 7468 6520 6861 7463 682e 0a0a 2020 202d the hatch... -\n+00019ab0: 2d2d 2d2d 2d2d 2d2d 2d20 466f 6f74 6e6f --------- Footno\n+00019ac0: 7465 7320 2d2d 2d2d 2d2d 2d2d 2d2d 0a0a tes ----------..\n+00019ad0: 2020 2028 3129 2049 206b 6e6f 7720 686f (1) I know ho\n+00019ae0: 7720 746f 2066 6978 2074 6869 7320 7072 w to fix this pr\n+00019af0: 6f62 6c65 6d2c 2062 7574 2049 2064 6f6e oblem, but I don\n+00019b00: 2774 206c 696b 6520 6d79 2073 6f6c 7574 't like my solut\n+00019b10: 696f 6e2c 2061 6e64 0a49 276d 2069 6e74 ion, and.I'm int\n+00019b20: 6572 6573 7465 6420 696e 2079 6f75 7273 erested in yours\n+00019b30: 2e0a 0a1f 0a46 696c 653a 2073 6b65 7463 .....File: sketc\n+00019b40: 682e 696e 666f 2c20 204e 6f64 653a 2043 h.info, Node: C\n+00019b50: 6f6d 6d61 6e64 206c 696e 652c 2020 4e65 ommand line, Ne\n+00019b60: 7874 3a20 496e 7374 616c 6c69 6e67 2073 xt: Installing s\n+00019b70: 6b65 7463 682c 2020 5072 6576 3a20 4275 ketch, Prev: Bu\n+00019b80: 696c 6469 6e67 2061 2064 7261 7769 6e67 ilding a drawing\n+00019b90: 2c20 2055 703a 2054 6f70 0a0a 3520 436f , Up: Top..5 Co\n+00019ba0: 6d6d 616e 6420 6c69 6e65 0a2a 2a2a 2a2a mmand line.*****\n+00019bb0: 2a2a 2a2a 2a2a 2a2a 2a0a 0a2a 5379 6e6f *********..*Syno\n+00019bc0: 7073 6973 3a2a 0a20 2020 2020 736b 6574 psis:*. sket\n+00019bd0: 6368 205b 2d68 5d5b 2d56 2078 2e79 5d5b ch [-h][-V x.y][\n+00019be0: 2d76 5d5b 2d62 5d5b 2d64 5d5b 7420 646f -v][-b][-d][t do\n+00019bf0: 6374 6d70 5d5b 2d54 5b75 7c65 5d5b 705b ctmp][-T[u|e][p[\n+00019c00: 507c 545d 5b4c 7c43 5d5d 5d5b 2d6f 206f P|T][L|C]]][-o o\n+00019c10: 7574 7075 742e 7465 785d 0a20 2020 2020 utput.tex]. \n+00019c20: 2020 5b2d 4420 5441 4720 2e2e 2e5d 2069 [-D TAG ...] i\n+00019c30: 6e70 7574 312e 736b 205b 2d55 2054 4147 nput1.sk [-U TAG\n+00019c40: 202e 2e2e 5d20 696e 7075 7432 2e73 6b20 ...] input2.sk \n+00019c50: 2e2e 2e0a 0a2a 4465 7363 7269 7074 696f .....*Descriptio\n+00019c60: 6e2a 2050 726f 6365 7373 6573 2074 6865 n* Processes the\n+00019c70: 20e2 8098 736b 6574 6368 e280 9920 696e ...sketch... in\n+00019c80: 7075 7420 6669 6c65 7320 696e 206f 7264 put files in ord\n+00019c90: 6572 2074 6f20 7072 6f64 7563 650a e280 er to produce...\n+00019ca0: 9850 5354 7269 636b 73e2 8099 206f 7574 .PSTricks... out\n+00019cb0: 7075 7420 636f 6465 2073 7569 7461 626c put code suitabl\n+00019cc0: 6520 666f 7220 696e 636c 7573 696f 6e20 e for inclusion \n+00019cd0: 696e 2061 2054 6558 206f 7220 4c61 5465 in a TeX or LaTe\n+00019ce0: 580a 646f 6375 6d65 6e74 2e0a 0a2a 4f70 X.document...*Op\n+00019cf0: 7469 6f6e 733a 2a0a e280 982d 68e2 8099 tions:*....-h...\n+00019d00: 0a20 2020 2020 5072 696e 7420 6120 7368 . Print a sh\n+00019d10: 6f72 7420 6361 7461 6c6f 6720 6f66 206f ort catalog of o\n+00019d20: 7074 696f 6e73 2e0a e280 982d 56e2 8099 ptions.....-V...\n+00019d30: 0a20 2020 2020 5365 7420 7468 6520 e280 . Set the ..\n+00019d40: 9850 5354 7269 636b 73e2 8099 2076 6572 .PSTricks... ver\n+00019d50: 7369 6f6e 2061 7373 756d 6564 2066 6f72 sion assumed for\n+00019d60: 206f 7574 7075 7420 7075 7270 6f73 6573 output purposes\n+00019d70: 2074 6f20 e280 9878 2e79 e280 992c 0a20 to ...x.y...,. \n+00019d80: 2020 2020 666f 7220 6578 616d 706c 6520 for example \n+00019d90: 312e 3139 2e20 2055 7375 616c 6c79 206e 1.19. Usually n\n+00019da0: 6565 6465 6420 6f6e 6c79 2069 6620 796f eeded only if yo\n+00019db0: 7572 20e2 8098 5053 5472 6963 6b73 e280 ur ...PSTricks..\n+00019dc0: 9920 6973 206f 6c64 0a20 2020 2020 636f . is old. co\n+00019dd0: 6d70 6172 6564 2074 6f20 796f 7572 20e2 mpared to your .\n+00019de0: 8098 736b 6574 6368 e280 992e 2020 5573 ..sketch.... Us\n+00019df0: 6520 e280 982d 76e2 8099 2074 6f20 7365 e ...-v... to se\n+00019e00: 6520 7768 6174 20e2 8098 736b 6574 6368 e what ...sketch\n+00019e10: e280 9920 6173 7375 6d65 730a 2020 2020 ... assumes. \n+00019e20: 2062 7920 6465 6661 756c 742e 0ae2 8098 by default.....\n+00019e30: 2d76 e280 990a 2020 2020 2050 7269 6e74 -v.... Print\n+00019e40: 2076 6572 7369 6f6e 2069 6e66 6f72 6d61 version informa\n+00019e50: 7469 6f6e 2074 6f20 7374 616e 6461 7264 tion to standard\n+00019e60: 206f 7574 7075 742c 2069 6e63 6c75 6469 output, includi\n+00019e70: 6e67 2074 6865 2076 6572 7369 6f6e 0a20 ng the version. \n+00019e80: 2020 2020 6f66 20e2 8098 5053 5472 6963 of ...PSTric\n+00019e90: 6b73 e280 9920 6173 7375 6d65 6420 666f ks... assumed fo\n+00019ea0: 7220 6f75 7470 7574 2028 6361 6e20 6265 r output (can be\n+00019eb0: 2063 6861 6e67 6564 2077 6974 6820 e280 changed with ..\n+00019ec0: 982d 56e2 8099 2061 626f 7665 292e 0ae2 .-V... above)...\n+00019ed0: 8098 2d62 e280 990a 2020 2020 2055 7365 ..-b.... Use\n+00019ee0: 2061 2042 5350 2028 2a4e 6f74 6520 4869 a BSP (*Note Hi\n+00019ef0: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n+00019f00: 6f76 616c 3a3a 2e29 2020 666f 7220 5f61 oval::.) for _a\n+00019f10: 6c6c 5f20 6869 6464 656e 0a20 2020 2020 ll_ hidden. \n+00019f20: 7375 7266 6163 6520 7265 6d6f 7661 6c20 surface removal \n+00019f30: 7261 7468 6572 2074 6861 6e20 7468 6520 rather than the \n+00019f40: 6465 6661 756c 742c 2077 6869 6368 2069 default, which i\n+00019f50: 7320 7468 6520 6465 7074 6820 736f 7274 s the depth sort\n+00019f60: 0a20 2020 2020 616c 676f 7269 7468 6d20 . algorithm \n+00019f70: 7769 7468 2042 5350 7320 7573 6564 206f with BSPs used o\n+00019f80: 6e6c 7920 666f 7220 6379 636c 6520 7265 nly for cycle re\n+00019f90: 736f 6c75 7469 6f6e 2e20 2054 6869 7320 solution. This \n+00019fa0: 6d61 790a 2020 2020 2070 726f 6475 6365 may. produce\n+00019fb0: 2063 6f72 7265 6374 206f 7574 7075 7420 correct output \n+00019fc0: 696e 2063 6572 7461 696e 2064 6567 656e in certain degen\n+00019fd0: 6572 6174 6520 6361 7365 7320 7768 6572 erate cases wher\n+00019fe0: 6520 7468 6520 6465 7074 680a 2020 2020 e the depth. \n+00019ff0: 2073 6f72 7420 6361 6e6e 6f74 2c20 6275 sort cannot, bu\n+0001a000: 7420 6974 2061 6c73 6f20 6c65 6164 7320 t it also leads \n+0001a010: 746f 206d 616e 7920 6772 6174 7569 746f to many gratuito\n+0001a020: 7573 2073 706c 6974 732c 2068 656e 6365 us splits, hence\n+0001a030: 0a20 2020 2020 6d6f 7265 2061 6e6f 6d61 . more anoma\n+0001a040: 6c69 6573 202a 6e6f 7465 2042 7567 7320 lies *note Bugs \n+0001a050: 616e 6420 616e 6f6d 616c 6965 733a 3a20 and anomalies:: \n+0001a060: 616e 6420 6269 6720 6f75 7470 7574 2066 and big output f\n+0001a070: 696c 6573 2e0a e280 982d 64e2 8099 0a20 iles.....-d.... \n+0001a080: 2020 2020 5275 6e20 e280 9873 6b65 7463 Run ...sketc\n+0001a090: 68e2 8099 2773 2070 6172 7365 7220 696e h...'s parser in\n+0001a0a0: 2064 6562 7567 6769 6e67 206d 6f64 652e debugging mode.\n+0001a0b0: 2020 5468 6973 2069 7320 7072 696d 6172 This is primar\n+0001a0c0: 696c 7920 666f 720a 2020 2020 2064 6576 ily for. dev\n+0001a0d0: 656c 6f70 6d65 6e74 2e0a e280 982d 74e2 elopment.....-t.\n+0001a0e0: 8099 0a20 2020 2020 5573 6520 636f 6e74 ... Use cont\n+0001a0f0: 656e 7473 206f 6620 6669 6c65 20e2 8098 ents of file ...\n+0001a100: 646f 6374 6d70 e280 9920 6173 2061 2064 doctmp... as a d\n+0001a110: 6f63 756d 656e 7420 7465 6d70 6c61 7465 ocument template\n+0001a120: 2069 6e20 7768 6963 6820 746f 0a20 2020 in which to. \n+0001a130: 2020 656e 636c 6f73 6520 e280 9850 5354 enclose ...PST\n+0001a140: 7269 636b 73e2 8099 206f 7574 7075 7420 ricks... output \n+0001a150: 636f 6465 2e20 2054 6865 2063 6f64 6520 code. The code \n+0001a160: 6973 2069 6e73 6572 7465 6420 696e 2070 is inserted in p\n+0001a170: 6c61 6365 206f 660a 2020 2020 2074 6865 lace of. the\n+0001a180: 2066 6972 7374 2069 6e73 7461 6e63 6520 first instance \n+0001a190: 6f66 2074 6865 2065 7363 6170 6520 7374 of the escape st\n+0001a1a0: 7269 6e67 2025 2553 4b45 5443 485f 4f55 ring %%SKETCH_OU\n+0001a1b0: 5450 5554 2525 2e0a e280 982d 54e2 8099 TPUT%%.....-T...\n+0001a1c0: 0a20 2020 2020 4361 7573 6573 20e2 8098 . Causes ...\n+0001a1d0: 5053 5472 6963 6b73 e280 9920 6f75 7470 PSTricks... outp\n+0001a1e0: 7574 2074 6f20 6265 2065 6e63 6c6f 7365 ut to be enclose\n+0001a1f0: 6420 696e 2064 6566 6175 6c74 2055 5320 d in default US \n+0001a200: 646f 6375 6d65 6e74 0a20 2020 2020 7465 document. te\n+0001a210: 6d70 6c61 7465 2074 6578 742e 2020 4f70 mplate text. Op\n+0001a220: 7469 6f6e 20e2 8098 2d54 75e2 8099 2069 tion ...-Tu... i\n+0001a230: 7320 6120 7379 6e6f 6e79 6d2e 2020 4f70 s a synonym. Op\n+0001a240: 7469 6f6e 20e2 8098 2d54 65e2 8099 2063 tion ...-Te... c\n+0001a250: 6175 7365 7320 7468 650a 2020 2020 2045 auses the. E\n+0001a260: 7572 6f20 7374 616e 6461 7264 2064 6f63 uro standard doc\n+0001a270: 756d 656e 7420 7465 6d70 6c61 7465 2074 ument template t\n+0001a280: 6f20 6265 2075 7365 642e 2020 4120 e280 o be used. A ..\n+0001a290: 9870 e280 9920 6170 7065 6e64 6564 2074 .p... appended t\n+0001a2a0: 6f20 616e 790a 2020 2020 206f 6620 7468 o any. of th\n+0001a2b0: 6573 6520 6f70 7469 6f6e 7320 6361 7573 ese options caus\n+0001a2c0: 6573 2074 6865 2072 6573 7065 6374 6976 es the respectiv\n+0001a2d0: 6520 6465 6661 756c 7420 e280 9850 5354 e default ...PST\n+0001a2e0: 7269 636b 73e2 8099 2064 6f63 756d 656e ricks... documen\n+0001a2f0: 740a 2020 2020 2074 656d 706c 6174 6520 t. template \n+0001a300: 746f 2062 6520 7072 696e 7465 6420 746f to be printed to\n+0001a310: 2073 7461 6e64 6172 6420 6f75 7470 7574 standard output\n+0001a320: 2e20 2041 6e20 6170 7065 6e64 6564 20e2 . An appended .\n+0001a330: 8098 50e2 8099 2069 7320 610a 2020 2020 ..P... is a. \n+0001a340: 2073 796e 6f6e 796d 2e20 2041 6e20 6170 synonym. 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This tool \n+0001b130: 6973 2061 7661 696c 6162 6c65 2069 6e0a is available in.\n+0001b140: 6269 6e61 7279 2066 6f72 6d20 666f 7220 binary form for \n+0001b150: 5769 6e64 6f77 732c 2061 6e64 2069 7420 Windows, and it \n+0001b160: 6275 696c 6473 2065 6173 696c 7920 7769 builds easily wi\n+0001b170: 7468 2061 2073 696d 706c 6520 e280 986d th a simple ...m\n+0001b180: 616b 65e2 8099 2075 6e64 6572 0a6c 696e ake... under.lin\n+0001b190: 7578 206f 7220 4379 6777 696e 2069 6e73 ux or Cygwin ins\n+0001b1a0: 7461 6c6c 6174 696f 6e73 2074 6861 7420 tallations that \n+0001b1b0: 6861 7665 2064 6576 656c 6f70 6d65 6e74 have development\n+0001b1c0: 2074 6f6f 6c73 2069 6e73 7461 6c6c 6564 tools installed\n+0001b1d0: 206f 720a 756e 6465 7220 e280 984d 6163 or.under ...Mac\n+0001b1e0: 204f 5320 58e2 8099 2077 6974 6820 e280 OS X... with ..\n+0001b1f0: 9858 436f 6465 e280 9920 696e 7374 616c .XCode... instal\n+0001b200: 6c65 642e 0a0a 1f0a 4669 6c65 3a20 736b led.....File: sk\n+0001b210: 6574 6368 2e69 6e66 6f2c 2020 4e6f 6465 etch.info, Node\n+0001b220: 3a20 496e 6465 7820 6f66 2073 796e 7461 : Index of synta\n+0001b230: 782c 2020 4e65 7874 3a20 496e 6465 782c x, Next: Index,\n+0001b240: 2020 5072 6576 3a20 496e 7374 616c 6c69 Prev: Installi\n+0001b250: 6e67 2073 6b65 7463 682c 2020 5570 3a20 ng sketch, Up: \n+0001b260: 546f 700a 0a49 6e64 6578 206f 6620 7379 Top..Index of sy\n+0001b270: 6e74 6178 0a2a 2a2a 2a2a 2a2a 2a2a 2a2a ntax.***********\n+0001b280: 2a2a 2a2a 0a0a 0008 5b69 6e64 6578 0008 ****....[index..\n+0001b290: 5d0a 2a20 4d65 6e75 3a0a 0a2a 202d 2c20 ].* Menu:..* -, \n+0001b2a0: 6d69 6e75 7320 6f70 6572 6174 6f72 3a20 minus operator: \n+0001b2b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001b2c0: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n+0001b2d0: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+0001b2e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b2f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b310: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b320: 2028 6c69 6e65 2031 3529 0a2a 202d 2c20 (line 15).* -, \n-0001b330: 756e 6172 7920 6d69 6e75 7320 6f70 6572 unary minus oper\n-0001b340: 6174 6f72 3a20 2020 2020 2020 2020 2020 ator: \n-0001b350: 2020 2020 556e 6172 7920 666f 726d 732e Unary forms.\n-0001b360: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001b370: 3130 290a 2a20 2e2c 2064 6f74 206f 7065 10).* ., dot ope\n-0001b380: 7261 746f 723a 2020 2020 2020 2020 2020 rator: \n-0001b390: 2020 2020 2020 2020 2020 2020 2054 776f Two\n-0001b3a0: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n-0001b3b0: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n+0001b310: 2020 2020 2020 2020 2020 2020 2020 2028 (\n+0001b320: 6c69 6e65 2031 3529 0a2a 202d 2c20 756e line 15).* -, un\n+0001b330: 6172 7920 6d69 6e75 7320 6f70 6572 6174 ary minus operat\n+0001b340: 6f72 3a20 2020 2020 2020 2020 2020 2020 or: \n+0001b350: 2020 556e 6172 7920 666f 726d 732e 2020 Unary forms. \n+0001b360: 2020 2020 2020 2020 286c 696e 6520 3130 (line 10\n+0001b370: 290a 2a20 2e2c 2064 6f74 206f 7065 7261 ).* ., dot opera\n+0001b380: 746f 723a 2020 2020 2020 2020 2020 2020 tor: \n+0001b390: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n+0001b3a0: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n+0001b3b0: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n 0001b3c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b3d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b3e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b3f0: 2020 2020 2020 2020 286c 696e 6520 3139 (line 19\n-0001b400: 290a 2a20 2e2c 2064 6f74 206f 7065 7261 ).* ., dot opera\n-0001b410: 746f 7220 3c31 3e3a 2020 2020 2020 2020 tor <1>: \n-0001b420: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n-0001b430: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n-0001b440: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n+0001b3f0: 2020 2020 2020 286c 696e 6520 3139 290a (line 19).\n+0001b400: 2a20 2e2c 2064 6f74 206f 7065 7261 746f * ., dot operato\n+0001b410: 7220 3c31 3e3a 2020 2020 2020 2020 2020 r <1>: \n+0001b420: 2020 2020 2020 2020 2054 776f 2d6f 7065 Two-ope\n+0001b430: 7261 6e64 2028 6269 6e61 7279 2920 666f rand (binary) fo\n+0001b440: 726d 732e 0a20 2020 2020 2020 2020 2020 rms.. \n 0001b450: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b460: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b480: 2020 2020 2020 286c 696e 6520 3631 290a (line 61).\n-0001b490: 2a20 2778 2c20 2779 2c20 616e 6420 277a * 'x, 'y, and 'z\n-0001b4a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001b4b0: 2020 2020 2020 2020 2041 6666 696e 6520 Affine \n-0001b4c0: 6172 6974 686d 6574 6963 2e20 2020 2028 arithmetic. (\n-0001b4d0: 6c69 6e65 2033 3729 0a2a 2027 782c 2027 line 37).* 'x, '\n-0001b4e0: 792c 2061 6e64 2027 7a20 3c31 3e3a 2020 y, and 'z <1>: \n+0001b480: 2020 2020 286c 696e 6520 3631 290a 2a20 (line 61).* \n+0001b490: 2778 2c20 2779 2c20 616e 6420 277a 3a20 'x, 'y, and 'z: \n+0001b4a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001b4b0: 2020 2020 2020 2041 6666 696e 6520 6172 Affine ar\n+0001b4c0: 6974 686d 6574 6963 2e20 2020 2028 6c69 ithmetic. (li\n+0001b4d0: 6e65 2033 3729 0a2a 2027 782c 2027 792c ne 37).* 'x, 'y,\n+0001b4e0: 2061 6e64 2027 7a20 3c31 3e3a 2020 2020 and 'z <1>: \n 0001b4f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b500: 2020 5477 6f2d 6f70 6572 616e 6420 2862 Two-operand (b\n-0001b510: 696e 6172 7929 2066 6f72 6d73 2e0a 2020 inary) forms.. \n+0001b500: 5477 6f2d 6f70 6572 616e 6420 2862 696e Two-operand (bin\n+0001b510: 6172 7929 2066 6f72 6d73 2e0a 2020 2020 ary) forms.. \n 0001b520: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b530: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b540: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b550: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001b560: 6e65 2034 3129 0a2a 2028 2029 2c20 6772 ne 41).* ( ), gr\n-0001b570: 6f75 7069 6e67 3a20 2020 2020 2020 2020 ouping: \n-0001b580: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b590: 5477 6f2d 6f70 6572 616e 6420 2862 696e Two-operand (bin\n-0001b5a0: 6172 7929 2066 6f72 6d73 2e0a 2020 2020 ary) forms.. \n+0001b550: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001b560: 2034 3129 0a2a 2028 2029 2c20 6772 6f75 41).* ( ), grou\n+0001b570: 7069 6e67 3a20 2020 2020 2020 2020 2020 ping: \n+0001b580: 2020 2020 2020 2020 2020 2020 2020 5477 Tw\n+0001b590: 6f2d 6f70 6572 616e 6420 2862 696e 6172 o-operand (binar\n+0001b5a0: 7929 2066 6f72 6d73 2e0a 2020 2020 2020 y) forms.. \n 0001b5b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b5c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b5d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b5e0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001b5f0: 2035 3829 0a2a 2028 666f 6f29 2c20 706f 58).* (foo), po\n-0001b600: 696e 7420 7265 6665 7265 6e63 653a 2020 int reference: \n-0001b610: 2020 2020 2020 2020 2020 2020 2020 4472 Dr\n-0001b620: 6177 696e 6720 6120 736f 6c69 642e 2020 awing a solid. \n-0001b630: 2020 2020 286c 696e 6520 3234 290a 2a20 (line 24).* \n-0001b640: 2866 6f6f 292c 2070 6f69 6e74 2072 6566 (foo), point ref\n-0001b650: 6572 656e 6365 203c 313e 3a20 2020 2020 erence <1>: \n-0001b660: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n-0001b670: 7265 6665 7265 6e63 6573 2e20 2028 6c69 references. (li\n-0001b680: 6e65 2031 3429 0a2a 205b 5b20 5d5b 205d ne 14).* [[ ][ ]\n-0001b690: 5b20 5d5b 205d 5d2c 2074 7261 6e73 666f [ ][ ]], transfo\n-0001b6a0: 726d 206c 6974 6572 616c 3a20 2020 2020 rm literal: \n-0001b6b0: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-0001b6c0: 6c73 2e20 2020 286c 696e 6520 3437 290a ls. (line 47).\n-0001b6d0: 2a20 5b5b 205d 5b20 5d5b 205d 5b20 5d5d * [[ ][ ][ ][ ]]\n-0001b6e0: 2c20 7472 616e 7366 6f72 6d20 6c69 7465 , transform lite\n-0001b6f0: 7261 6c20 3c31 3e3a 2054 7261 6e73 666f ral <1>: Transfo\n-0001b700: 726d 206c 6974 6572 616c 732e 2020 2028 rm literals. (\n-0001b710: 6c69 6e65 2035 3329 0a2a 205b 5b66 6f6f line 53).* [[foo\n-0001b720: 5d5d 2c20 7472 616e 7366 6f72 6d20 7265 ]], transform re\n-0001b730: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n-0001b740: 2020 466f 726d 7320 6f66 2072 6566 6572 Forms of refer\n-0001b750: 656e 6365 732e 2020 286c 696e 6520 3136 ences. (line 16\n-0001b760: 290a 2a20 5b5b 666f 6f5d 5d2c 2074 7261 ).* [[foo]], tra\n-0001b770: 6e73 666f 726d 2072 6566 6572 656e 6365 nsform reference\n-0001b780: 203c 313e 3a20 2020 2020 204f 7665 7276 <1>: Overv\n-0001b790: 6965 772e 2020 2020 2020 2020 2020 2020 iew. \n-0001b7a0: 2028 6c69 6e65 2033 3529 0a2a 205b 5b66 (line 35).* [[f\n-0001b7b0: 6f6f 5d5d 2c20 7472 616e 7366 6f72 6d20 oo]], transform \n-0001b7c0: 7265 6665 7265 6e63 6520 3c32 3e3a 2020 reference <2>: \n-0001b7d0: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n-0001b7e0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001b7f0: 3335 290a 2a20 5b66 6f6f 2c2e 2e2e 2c62 35).* [foo,...,b\n-0001b800: 6172 5d2c 206d 756c 7469 706c 6520 6f70 ar], multiple op\n-0001b810: 7469 6f6e 7320 7265 6665 7265 6e63 653a tions reference:\n-0001b820: 2046 6f72 6d73 206f 6620 7265 6665 7265 Forms of refere\n-0001b830: 6e63 6573 2e0a 2020 2020 2020 2020 2020 nces.. \n+0001b5e0: 2020 2020 2020 2020 2028 6c69 6e65 2035 (line 5\n+0001b5f0: 3829 0a2a 2028 666f 6f29 2c20 706f 696e 8).* (foo), poin\n+0001b600: 7420 7265 6665 7265 6e63 653a 2020 2020 t reference: \n+0001b610: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n+0001b620: 696e 6720 6120 736f 6c69 642e 2020 2020 ing a solid. \n+0001b630: 2020 286c 696e 6520 3234 290a 2a20 2866 (line 24).* (f\n+0001b640: 6f6f 292c 2070 6f69 6e74 2072 6566 6572 oo), point refer\n+0001b650: 656e 6365 203c 313e 3a20 2020 2020 2020 ence <1>: \n+0001b660: 2020 2020 2046 6f72 6d73 206f 6620 7265 Forms of re\n+0001b670: 6665 7265 6e63 6573 2e20 2028 6c69 6e65 ferences. (line\n+0001b680: 2031 3429 0a2a 205b 5b20 5d5b 205d 5b20 14).* [[ ][ ][ \n+0001b690: 5d5b 205d 5d2c 2074 7261 6e73 666f 726d ][ ]], transform\n+0001b6a0: 206c 6974 6572 616c 3a20 2020 2020 5472 literal: Tr\n+0001b6b0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+0001b6c0: 2e20 2020 286c 696e 6520 3437 290a 2a20 . (line 47).* \n+0001b6d0: 5b5b 205d 5b20 5d5b 205d 5b20 5d5d 2c20 [[ ][ ][ ][ ]], \n+0001b6e0: 7472 616e 7366 6f72 6d20 6c69 7465 7261 transform litera\n+0001b6f0: 6c20 3c31 3e3a 2054 7261 6e73 666f 726d l <1>: Transform\n+0001b700: 206c 6974 6572 616c 732e 2020 2028 6c69 literals. (li\n+0001b710: 6e65 2035 3329 0a2a 205b 5b66 6f6f 5d5d ne 53).* [[foo]]\n+0001b720: 2c20 7472 616e 7366 6f72 6d20 7265 6665 , transform refe\n+0001b730: 7265 6e63 653a 2020 2020 2020 2020 2020 rence: \n+0001b740: 466f 726d 7320 6f66 2072 6566 6572 656e Forms of referen\n+0001b750: 6365 732e 2020 286c 696e 6520 3136 290a ces. (line 16).\n+0001b760: 2a20 5b5b 666f 6f5d 5d2c 2074 7261 6e73 * [[foo]], trans\n+0001b770: 666f 726d 2072 6566 6572 656e 6365 203c form reference <\n+0001b780: 313e 3a20 2020 2020 204f 7665 7276 6965 1>: Overvie\n+0001b790: 772e 2020 2020 2020 2020 2020 2020 2028 w. (\n+0001b7a0: 6c69 6e65 2033 3529 0a2a 205b 5b66 6f6f line 35).* [[foo\n+0001b7b0: 5d5d 2c20 7472 616e 7366 6f72 6d20 7265 ]], transform re\n+0001b7c0: 6665 7265 6e63 6520 3c32 3e3a 2020 2020 ference <2>: \n+0001b7d0: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n+0001b7e0: 2020 2020 2020 2020 286c 696e 6520 3335 (line 35\n+0001b7f0: 290a 2a20 5b66 6f6f 2c2e 2e2e 2c62 6172 ).* [foo,...,bar\n+0001b800: 5d2c 206d 756c 7469 706c 6520 6f70 7469 ], multiple opti\n+0001b810: 6f6e 7320 7265 6665 7265 6e63 653a 2046 ons reference: F\n+0001b820: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n+0001b830: 6573 2e0a 2020 2020 2020 2020 2020 2020 es.. \n 0001b840: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b850: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b860: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b870: 2020 2020 2028 6c69 6e65 2031 3829 0a2a (line 18).*\n-0001b880: 205b 666f 6f5d 2c20 6f70 7469 6f6e 7320 [foo], options \n-0001b890: 7265 6665 7265 6e63 653a 2020 2020 2020 reference: \n-0001b8a0: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n-0001b8b0: 2073 7765 6570 7320 7769 7468 2063 6c6f sweeps with clo\n-0001b8c0: 7375 7265 2e0a 2020 2020 2020 2020 2020 sure.. \n+0001b870: 2020 2028 6c69 6e65 2031 3829 0a2a 205b (line 18).* [\n+0001b880: 666f 6f5d 2c20 6f70 7469 6f6e 7320 7265 foo], options re\n+0001b890: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n+0001b8a0: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n+0001b8b0: 7765 6570 7320 7769 7468 2063 6c6f 7375 weeps with closu\n+0001b8c0: 7265 2e0a 2020 2020 2020 2020 2020 2020 re.. \n 0001b8d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b8e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001b8f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001b900: 2020 2020 2028 6c69 6e65 2032 3429 0a2a (line 24).*\n-0001b910: 205b 666f 6f5d 2c20 6f70 7469 6f6e 7320 [foo], options \n-0001b920: 7265 6665 7265 6e63 6520 3c31 3e3a 2020 reference <1>: \n-0001b930: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n-0001b940: 2072 6566 6572 656e 6365 732e 2020 286c references. (l\n-0001b950: 696e 6520 3138 290a 2a20 5b66 6f6f 5d2c ine 18).* [foo],\n-0001b960: 2076 6563 746f 7220 7265 6665 7265 6e63 vector referenc\n-0001b970: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-0001b980: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n-0001b990: 2e20 2020 2020 2028 6c69 6e65 2032 3029 . (line 20)\n-0001b9a0: 0a2a 205b 666f 6f5d 2c20 7665 6374 6f72 .* [foo], vector\n-0001b9b0: 2072 6566 6572 656e 6365 203c 313e 3a20 reference <1>: \n-0001b9c0: 2020 2020 2020 2020 2020 466f 726d 7320 Forms \n-0001b9d0: 6f66 2072 6566 6572 656e 6365 732e 2020 of references. \n-0001b9e0: 286c 696e 6520 3135 290a 2a20 7b20 7d2c (line 15).* { },\n-0001b9f0: 2062 6c6f 636b 2064 7261 7761 626c 653a block drawable:\n+0001b900: 2020 2028 6c69 6e65 2032 3429 0a2a 205b (line 24).* [\n+0001b910: 666f 6f5d 2c20 6f70 7469 6f6e 7320 7265 foo], options re\n+0001b920: 6665 7265 6e63 6520 3c31 3e3a 2020 2020 ference <1>: \n+0001b930: 2020 2020 2020 466f 726d 7320 6f66 2072 Forms of r\n+0001b940: 6566 6572 656e 6365 732e 2020 286c 696e eferences. (lin\n+0001b950: 6520 3138 290a 2a20 5b66 6f6f 5d2c 2076 e 18).* [foo], v\n+0001b960: 6563 746f 7220 7265 6665 7265 6e63 653a ector reference:\n+0001b970: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+0001b980: 6f6c 796c 696e 6520 7377 6565 7073 2e20 olyline sweeps. \n+0001b990: 2020 2020 2028 6c69 6e65 2032 3029 0a2a (line 20).*\n+0001b9a0: 205b 666f 6f5d 2c20 7665 6374 6f72 2072 [foo], vector r\n+0001b9b0: 6566 6572 656e 6365 203c 313e 3a20 2020 eference <1>: \n+0001b9c0: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n+0001b9d0: 2072 6566 6572 656e 6365 732e 2020 286c references. (l\n+0001b9e0: 696e 6520 3135 290a 2a20 7b20 7d2c 2062 ine 15).* { }, b\n+0001b9f0: 6c6f 636b 2064 7261 7761 626c 653a 2020 lock drawable: \n 0001ba00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ba10: 2020 204f 626a 6563 7420 7472 616e 7366 Object transf\n-0001ba20: 6f72 6d73 2e20 2020 2028 6c69 6e65 2032 orms. (line 2\n-0001ba30: 3429 0a2a 207b 207d 2c20 626c 6f63 6b20 4).* { }, block \n-0001ba40: 6472 6177 6162 6c65 203c 313e 3a20 2020 drawable <1>: \n-0001ba50: 2020 2020 2020 2020 2020 2020 4e65 7374 Nest\n-0001ba60: 6564 2073 7765 6570 732e 2020 2020 2020 ed sweeps. \n-0001ba70: 2020 286c 696e 6520 3235 290a 2a20 7b20 (line 25).* { \n-0001ba80: 7d2c 2062 6c6f 636b 2064 7261 7761 626c }, block drawabl\n-0001ba90: 6520 3c32 3e3a 2020 2020 2020 2020 2020 e <2>: \n-0001baa0: 2020 2020 2053 7765 7074 2062 6c6f 636b Swept block\n-0001bab0: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-0001bac0: 2020 3729 0a2a 207b 207d 2c20 626c 6f63 7).* { }, bloc\n-0001bad0: 6b20 6472 6177 6162 6c65 203c 333e 3a20 k drawable <3>: \n-0001bae0: 2020 2020 2020 2020 2020 2020 2020 426c Bl\n-0001baf0: 6f63 6b73 2e20 2020 2020 2020 2020 2020 ocks. \n-0001bb00: 2020 2020 286c 696e 6520 2036 290a 2a20 (line 6).* \n-0001bb10: 7b20 7d2c 2062 6c6f 636b 2064 7261 7761 { }, block drawa\n-0001bb20: 626c 6520 3c34 3e3a 2020 2020 2020 2020 ble <4>: \n-0001bb30: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n-0001bb40: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001bb50: 6e65 2033 3729 0a2a 207b 666f 6f7d 2c20 ne 37).* {foo}, \n-0001bb60: 6472 6177 6162 6c65 2072 6566 6572 656e drawable referen\n-0001bb70: 6365 3a20 2020 2020 2020 2020 2020 2020 ce: \n-0001bb80: 4f62 6a65 6374 2074 7261 6e73 666f 726d Object transform\n-0001bb90: 732e 2020 2020 286c 696e 6520 3333 290a s. (line 33).\n-0001bba0: 2a20 7b66 6f6f 7d2c 2064 7261 7761 626c * {foo}, drawabl\n-0001bbb0: 6520 7265 6665 7265 6e63 6520 3c31 3e3a e reference <1>:\n-0001bbc0: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n-0001bbd0: 6620 7265 6665 7265 6e63 6573 2e20 2028 f references. 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(line \n+0001c380: 3238 290a 2a20 6172 726f 7773 203c 323e 28).* arrows <2>\n+0001c390: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001c3a0: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n+0001c3b0: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n+0001c3c0: 2020 2028 6c69 6e65 2036 3929 0a2a 2061 (line 69).* a\n+0001c3d0: 7272 6f77 7320 3c33 3e3a 2020 2020 2020 rrows <3>: \n 0001c3e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c3f0: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n-0001c400: 6361 6c20 6472 6177 696e 672e 2020 286c cal drawing. (l\n-0001c410: 696e 6520 3236 290a 2a20 6172 726f 7773 ine 26).* arrows\n-0001c420: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n-0001c430: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c440: 2041 2074 6563 686e 6963 616c 2064 7261 A technical dra\n-0001c450: 7769 6e67 2e20 2028 6c69 6e65 2036 3829 wing. (line 68)\n-0001c460: 0a2a 2061 7369 6e3a 2020 2020 2020 2020 .* asin: \n+0001c3f0: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n+0001c400: 6c20 6472 6177 696e 672e 2020 286c 696e l drawing. (lin\n+0001c410: 6520 3236 290a 2a20 6172 726f 7773 203c e 26).* arrows <\n+0001c420: 343e 3a20 2020 2020 2020 2020 2020 2020 4>: \n+0001c430: 2020 2020 2020 2020 2020 2020 2020 2041 A\n+0001c440: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n+0001c450: 6e67 2e20 2028 6c69 6e65 2036 3829 0a2a ng. (line 68).*\n+0001c460: 2061 7369 6e3a 2020 2020 2020 2020 2020 asin: \n 0001c470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c480: 2020 2020 2020 2020 2020 556e 6172 7920 Unary \n-0001c490: 666f 726d 732e 2020 2020 2020 2020 2020 forms. \n-0001c4a0: 286c 696e 6520 3137 290a 2a20 6174 616e (line 17).* atan\n-0001c4b0: 323a 2020 2020 2020 2020 2020 2020 2020 2: \n+0001c480: 2020 2020 2020 2020 556e 6172 7920 666f Unary fo\n+0001c490: 726d 732e 2020 2020 2020 2020 2020 286c rms. (l\n+0001c4a0: 696e 6520 3137 290a 2a20 6174 616e 323a ine 17).* atan2:\n+0001c4b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001c4c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c4d0: 2020 2055 6e61 7279 2066 6f72 6d73 2e20 Unary forms. \n-0001c4e0: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n-0001c4f0: 3929 0a2a 2063 616d 6572 613a 2020 2020 9).* camera: \n+0001c4d0: 2055 6e61 7279 2066 6f72 6d73 2e20 2020 Unary forms. \n+0001c4e0: 2020 2020 2020 2028 6c69 6e65 2031 3929 (line 19)\n+0001c4f0: 0a2a 2063 616d 6572 613a 2020 2020 2020 .* camera: \n 0001c500: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c510: 2020 2020 2020 2020 2020 2020 4361 6d65 Came\n-0001c520: 7261 2e20 2020 2020 2020 2020 2020 2020 ra. \n-0001c530: 2020 286c 696e 6520 2036 290a 2a20 636f (line 6).* co\n-0001c540: 6e74 6578 743a 2020 2020 2020 2020 2020 ntext: \n+0001c510: 2020 2020 2020 2020 2020 4361 6d65 7261 Camera\n+0001c520: 2e20 2020 2020 2020 2020 2020 2020 2020 . \n+0001c530: 286c 696e 6520 2036 290a 2a20 636f 6e74 (line 6).* cont\n+0001c540: 6578 743a 2020 2020 2020 2020 2020 2020 ext: \n 0001c550: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c560: 2020 2020 204c 616e 6775 6167 652e 2020 Language. \n-0001c570: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001c580: 2031 3729 0a2a 2063 6f73 3a20 2020 2020 17).* cos: \n+0001c560: 2020 204c 616e 6775 6167 652e 2020 2020 Language. \n+0001c570: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n+0001c580: 3729 0a2a 2063 6f73 3a20 2020 2020 2020 7).* cos: \n 0001c590: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c5a0: 2020 2020 2020 2020 2020 2020 2020 556e Un\n-0001c5b0: 6172 7920 666f 726d 732e 2020 2020 2020 ary forms. \n-0001c5c0: 2020 2020 286c 696e 6520 3136 290a 2a20 (line 16).* \n-0001c5d0: 6375 6c6c 3a20 2020 2020 2020 2020 2020 cull: \n+0001c5a0: 2020 2020 2020 2020 2020 2020 556e 6172 Unar\n+0001c5b0: 7920 666f 726d 732e 2020 2020 2020 2020 y forms. \n+0001c5c0: 2020 286c 696e 6520 3136 290a 2a20 6375 (line 16).* cu\n+0001c5d0: 6c6c 3a20 2020 2020 2020 2020 2020 2020 ll: \n 0001c5e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c5f0: 2020 2020 2020 2044 7261 7769 6e67 2061 Drawing a\n-0001c600: 2073 6f6c 6964 2e20 2020 2020 2028 6c69 solid. (li\n-0001c610: 6e65 2034 3529 0a2a 2063 756c 6c20 3c31 ne 45).* cull <1\n-0001c620: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001c630: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c640: 506f 6c79 6c69 6e65 2073 7765 6570 732e Polyline sweeps.\n-0001c650: 2020 2020 2020 286c 696e 6520 2039 290a (line 9).\n-0001c660: 2a20 6375 6c6c 203c 323e 3a20 2020 2020 * cull <2>: \n+0001c5f0: 2020 2020 2044 7261 7769 6e67 2061 2073 Drawing a s\n+0001c600: 6f6c 6964 2e20 2020 2020 2028 6c69 6e65 olid. (line\n+0001c610: 2034 3529 0a2a 2063 756c 6c20 3c31 3e3a 45).* cull <1>:\n+0001c620: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001c630: 2020 2020 2020 2020 2020 2020 2020 506f Po\n+0001c640: 6c79 6c69 6e65 2073 7765 6570 732e 2020 lyline sweeps. \n+0001c650: 2020 2020 286c 696e 6520 2039 290a 2a20 (line 9).* \n+0001c660: 6375 6c6c 203c 323e 3a20 2020 2020 2020 cull <2>: \n 0001c670: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c680: 2020 2020 2020 2020 2054 7261 6e73 7061 Transpa\n-0001c690: 7265 6e63 792e 2020 2020 2020 2020 2028 rency. (\n-0001c6a0: 6c69 6e65 2031 3529 0a2a 2063 756c 6c20 line 15).* cull \n-0001c6b0: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n+0001c680: 2020 2020 2020 2054 7261 6e73 7061 7265 Transpare\n+0001c690: 6e63 792e 2020 2020 2020 2020 2028 6c69 ncy. (li\n+0001c6a0: 6e65 2031 3529 0a2a 2063 756c 6c20 3c33 ne 15).* cull <3\n+0001c6b0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001c6c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c6d0: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n-0001c6e0: 6177 696e 672e 2020 286c 696e 6520 3230 awing. (line 20\n-0001c6f0: 290a 2a20 6375 6c6c 203c 343e 3a20 2020 ).* cull <4>: \n+0001c6d0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n+0001c6e0: 696e 672e 2020 286c 696e 6520 3230 290a ing. (line 20).\n+0001c6f0: 2a20 6375 6c6c 203c 343e 3a20 2020 2020 * cull <4>: \n 0001c700: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c710: 2020 2020 2020 2020 2020 2049 6e74 6572 Inter\n-0001c720: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020 nal options. \n-0001c730: 2028 6c69 6e65 2020 3729 0a2a 2063 756c (line 7).* cul\n-0001c740: 6c20 3c35 3e3a 2020 2020 2020 2020 2020 l <5>: \n+0001c710: 2020 2020 2020 2020 2049 6e74 6572 6e61 Interna\n+0001c720: 6c20 6f70 7469 6f6e 732e 2020 2020 2028 l options. (\n+0001c730: 6c69 6e65 2020 3729 0a2a 2063 756c 6c20 line 7).* cull \n+0001c740: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n 0001c750: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c760: 2020 2020 476c 6f62 616c 206f 7074 696f Global optio\n-0001c770: 6e73 2e20 2020 2020 2020 286c 696e 6520 ns. (line \n-0001c780: 3133 290a 2a20 6375 7276 653a 2020 2020 13).* curve: \n+0001c760: 2020 476c 6f62 616c 206f 7074 696f 6e73 Global options\n+0001c770: 2e20 2020 2020 2020 286c 696e 6520 3133 . (line 13\n+0001c780: 290a 2a20 6375 7276 653a 2020 2020 2020 ).* curve: \n 0001c790: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c7a0: 2020 2020 2020 2020 2020 2020 2043 7572 Cur\n-0001c7b0: 7665 732e 2020 2020 2020 2020 2020 2020 ves. \n-0001c7c0: 2020 2028 6c69 6e65 2020 3629 0a2a 2064 (line 6).* d\n-0001c7d0: 6566 3a20 2020 2020 2020 2020 2020 2020 ef: \n+0001c7a0: 2020 2020 2020 2020 2020 2043 7572 7665 Curve\n+0001c7b0: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n+0001c7c0: 2028 6c69 6e65 2020 3629 0a2a 2064 6566 (line 6).* def\n+0001c7d0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n 0001c7e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c7f0: 2020 2020 2020 4472 6177 696e 6720 6120 Drawing a \n-0001c800: 736f 6c69 642e 2020 2020 2020 286c 696e solid. (lin\n-0001c810: 6520 2039 290a 2a20 6465 6620 3c31 3e3a e 9).* def <1>:\n+0001c7f0: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n+0001c800: 6c69 642e 2020 2020 2020 286c 696e 6520 lid. (line \n+0001c810: 2039 290a 2a20 6465 6620 3c31 3e3a 2020 9).* def <1>: \n 0001c820: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c830: 2020 2020 2020 2020 2020 2020 2020 2044 D\n-0001c840: 7261 7769 6e67 2061 2073 6f6c 6964 2e20 rawing a solid. \n-0001c850: 2020 2020 2028 6c69 6e65 2032 3229 0a2a (line 22).*\n-0001c860: 2064 6566 203c 323e 3a20 2020 2020 2020 def <2>: \n+0001c830: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n+0001c840: 7769 6e67 2061 2073 6f6c 6964 2e20 2020 wing a solid. \n+0001c850: 2020 2028 6c69 6e65 2032 3229 0a2a 2064 (line 22).* d\n+0001c860: 6566 203c 323e 3a20 2020 2020 2020 2020 ef <2>: \n 0001c870: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c880: 2020 2020 2020 2020 4f62 6a65 6374 2074 Object t\n-0001c890: 7261 6e73 666f 726d 732e 2020 2020 286c ransforms. (l\n-0001c8a0: 696e 6520 3130 290a 2a20 6465 6620 3c33 ine 10).* def <3\n-0001c8b0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001c8c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c8d0: 2050 6f69 6e74 2073 7765 6570 732e 2020 Point sweeps. \n-0001c8e0: 2020 2020 2020 2028 6c69 6e65 2031 3929 (line 19)\n-0001c8f0: 0a2a 2064 6566 203c 343e 3a20 2020 2020 .* def <4>: \n+0001c880: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n+0001c890: 6e73 666f 726d 732e 2020 2020 286c 696e nsforms. (lin\n+0001c8a0: 6520 3130 290a 2a20 6465 6620 3c33 3e3a e 10).* def <3>:\n+0001c8b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001c8c0: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+0001c8d0: 6f69 6e74 2073 7765 6570 732e 2020 2020 oint sweeps. \n+0001c8e0: 2020 2020 2028 6c69 6e65 2031 3929 0a2a (line 19).*\n+0001c8f0: 2064 6566 203c 343e 3a20 2020 2020 2020 def <4>: \n 0001c900: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c910: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n-0001c920: 6e65 2073 7765 6570 732e 2020 2020 2020 ne sweeps. \n-0001c930: 286c 696e 6520 2039 290a 2a20 6465 6620 (line 9).* def \n-0001c940: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n+0001c910: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n+0001c920: 2073 7765 6570 732e 2020 2020 2020 286c sweeps. (l\n+0001c930: 696e 6520 2039 290a 2a20 6465 6620 3c35 ine 9).* def <5\n+0001c940: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001c950: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c960: 2020 204e 6573 7465 6420 7377 6565 7073 Nested sweeps\n-0001c970: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n-0001c980: 3829 0a2a 2064 6566 203c 363e 3a20 2020 8).* def <6>: \n+0001c960: 204e 6573 7465 6420 7377 6565 7073 2e20 Nested sweeps. \n+0001c970: 2020 2020 2020 2028 6c69 6e65 2020 3829 (line 8)\n+0001c980: 0a2a 2064 6566 203c 363e 3a20 2020 2020 .* def <6>: \n 0001c990: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001c9a0: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-0001c9b0: 6c69 6e65 2073 7765 6570 7320 7769 7468 line sweeps with\n-0001c9c0: 2063 6c6f 7375 7265 2e0a 2020 2020 2020 closure.. \n+0001c9a0: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n+0001c9b0: 6e65 2073 7765 6570 7320 7769 7468 2063 ne sweeps with c\n+0001c9c0: 6c6f 7375 7265 2e0a 2020 2020 2020 2020 losure.. \n 0001c9d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001c9e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001c9f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca00: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n-0001ca10: 3029 0a2a 2064 6566 203c 373e 3a20 2020 0).* def <7>: \n+0001ca00: 2020 2020 2020 2028 6c69 6e65 2031 3029 (line 10)\n+0001ca10: 0a2a 2064 6566 203c 373e 3a20 2020 2020 .* def <7>: \n 0001ca20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca30: 2020 2020 2020 2020 2020 2020 4166 6669 Affi\n-0001ca40: 6e65 2061 7269 7468 6d65 7469 632e 2020 ne arithmetic. \n-0001ca50: 2020 286c 696e 6520 3131 290a 2a20 6465 (line 11).* de\n-0001ca60: 6620 3c38 3e3a 2020 2020 2020 2020 2020 f <8>: \n+0001ca30: 2020 2020 2020 2020 2020 4166 6669 6e65 Affine\n+0001ca40: 2061 7269 7468 6d65 7469 632e 2020 2020 arithmetic. \n+0001ca50: 286c 696e 6520 3131 290a 2a20 6465 6620 (line 11).* def \n+0001ca60: 3c38 3e3a 2020 2020 2020 2020 2020 2020 <8>: \n 0001ca70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ca80: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n-0001ca90: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001caa0: 2031 3229 0a2a 2064 6566 203c 393e 3a20 12).* def <9>: \n+0001ca80: 2020 204f 7665 7276 6965 772e 2020 2020 Overview. \n+0001ca90: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n+0001caa0: 3229 0a2a 2064 6566 203c 393e 3a20 2020 2).* def <9>: \n 0001cab0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cac0: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001cad0: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001cae0: 2020 2020 286c 696e 6520 3337 290a 2a20 (line 37).* \n-0001caf0: 6465 6620 3c31 303e 3a20 2020 2020 2020 def <10>: \n+0001cac0: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n+0001cad0: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n+0001cae0: 2020 286c 696e 6520 3337 290a 2a20 6465 (line 37).* de\n+0001caf0: 6620 3c31 303e 3a20 2020 2020 2020 2020 f <10>: \n 0001cb00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cb10: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n-0001cb20: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001cb30: 6e65 2036 3929 0a2a 2064 6566 203c 3131 ne 69).* def <11\n-0001cb40: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001cb50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cb60: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001cb70: 696e 672e 2020 286c 696e 6520 3134 290a ing. (line 14).\n-0001cb80: 2a20 6465 6620 3c31 323e 3a20 2020 2020 * def <12>: \n+0001cb10: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n+0001cb20: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001cb30: 2036 3929 0a2a 2064 6566 203c 3131 3e3a 69).* def <11>:\n+0001cb40: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001cb50: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+0001cb60: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+0001cb70: 672e 2020 286c 696e 6520 3134 290a 2a20 g. (line 14).* \n+0001cb80: 6465 6620 3c31 323e 3a20 2020 2020 2020 def <12>: \n 0001cb90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cba0: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001cbb0: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001cbc0: 6c69 6e65 2032 3629 0a2a 2064 6566 203c line 26).* def <\n-0001cbd0: 3133 3e3a 2020 2020 2020 2020 2020 2020 13>: \n+0001cba0: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001cbb0: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001cbc0: 6e65 2032 3629 0a2a 2064 6566 203c 3133 ne 26).* def <13\n+0001cbd0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n 0001cbe0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cbf0: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n-0001cc00: 6177 696e 672e 2020 286c 696e 6520 3431 awing. (line 41\n-0001cc10: 290a 2a20 6465 6620 3c31 343e 3a20 2020 ).* def <14>: \n+0001cbf0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n+0001cc00: 696e 672e 2020 286c 696e 6520 3431 290a ing. (line 41).\n+0001cc10: 2a20 6465 6620 3c31 343e 3a20 2020 2020 * def <14>: \n 0001cc20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cc30: 2020 2020 2020 2020 2020 2041 2074 6563 A tec\n-0001cc40: 686e 6963 616c 2064 7261 7769 6e67 2e20 hnical drawing. \n-0001cc50: 2028 6c69 6e65 2036 3829 0a2a 2064 6566 (line 68).* def\n-0001cc60: 203c 3135 3e3a 2020 2020 2020 2020 2020 <15>: \n+0001cc30: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n+0001cc40: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n+0001cc50: 6c69 6e65 2036 3829 0a2a 2064 6566 203c line 68).* def <\n+0001cc60: 3135 3e3a 2020 2020 2020 2020 2020 2020 15>: \n 0001cc70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cc80: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n-0001cc90: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n-0001cca0: 3935 290a 2a20 6465 6620 3c31 363e 3a20 95).* def <16>: \n+0001cc80: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n+0001cc90: 6177 696e 672e 2020 286c 696e 6520 3935 awing. (line 95\n+0001cca0: 290a 2a20 6465 6620 3c31 363e 3a20 2020 ).* def <16>: \n 0001ccb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ccc0: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n-0001ccd0: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n-0001cce0: 6c2e 2028 6c69 6e65 2031 3029 0a2a 2064 l. (line 10).* d\n-0001ccf0: 6566 203c 3137 3e3a 2020 2020 2020 2020 ef <17>: \n+0001ccc0: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n+0001ccd0: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n+0001cce0: 2028 6c69 6e65 2031 3029 0a2a 2064 6566 (line 10).* def\n+0001ccf0: 203c 3137 3e3a 2020 2020 2020 2020 2020 <17>: \n 0001cd00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001cd10: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n-0001cd20: 6963 616c 206d 6f64 656c 2e20 286c 696e ical model. (lin\n-0001cd30: 6520 3233 290a 2a20 6465 6620 3c31 383e e 23).* def <18>\n-0001cd40: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001cd50: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001cd60: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-0001cd70: 6465 6c2e 2028 6c69 6e65 2033 3229 0a2a del. (line 32).*\n-0001cd80: 2064 6f74 733a 2020 2020 2020 2020 2020 dots: \n+0001cd10: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n+0001cd20: 616c 206d 6f64 656c 2e20 286c 696e 6520 al model. (line \n+0001cd30: 3233 290a 2a20 6465 6620 3c31 383e 3a20 23).* def <18>: \n+0001cd40: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001cd50: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+0001cd60: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+0001cd70: 6c2e 2028 6c69 6e65 2033 3229 0a2a 2064 l. 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(line 12).* \n-0001d0a0: 696e 7075 743a 2020 2020 2020 2020 2020 input: \n+0001d070: 2020 2020 2020 2020 2020 2020 476c 6f62 Glob\n+0001d080: 616c 2065 6e76 6972 6f6e 6d65 6e74 2e20 al environment. \n+0001d090: 2020 286c 696e 6520 3132 290a 2a20 696e (line 12).* in\n+0001d0a0: 7075 743a 2020 2020 2020 2020 2020 2020 put: \n 0001d0b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d0c0: 2020 2020 2020 204c 616e 6775 6167 6520 Language \n-0001d0d0: 6261 7369 6373 2e20 2020 2020 2028 6c69 basics. (li\n-0001d0e0: 6e65 2031 3929 0a2a 2069 6e76 6572 7365 ne 19).* inverse\n-0001d0f0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001d100: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d110: 556e 6172 7920 666f 726d 732e 2020 2020 Unary forms. \n-0001d120: 2020 2020 2020 286c 696e 6520 3231 290a (line 21).\n-0001d130: 2a20 6c61 6e67 7561 6765 3a20 2020 2020 * language: \n+0001d0c0: 2020 2020 204c 616e 6775 6167 6520 6261 Language ba\n+0001d0d0: 7369 6373 2e20 2020 2020 2028 6c69 6e65 sics. 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(\n-0001d170: 6c69 6e65 2020 3629 0a2a 206c 6174 6578 line 6).* latex\n-0001d180: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001d150: 2020 2020 2020 204c 616e 6775 6167 652e Language.\n+0001d160: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+0001d170: 6e65 2020 3629 0a2a 206c 6174 6578 3a20 ne 6).* latex: \n+0001d180: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d190: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d1a0: 2020 4c61 6e67 7561 6765 2e20 2020 2020 Language. \n-0001d1b0: 2020 2020 2020 2020 286c 696e 6520 3137 (line 17\n-0001d1c0: 290a 2a20 6c61 793a 2020 2020 2020 2020 ).* lay: \n+0001d1a0: 4c61 6e67 7561 6765 2e20 2020 2020 2020 Language. \n+0001d1b0: 2020 2020 2020 286c 696e 6520 3137 290a (line 17).\n+0001d1c0: 2a20 6c61 793a 2020 2020 2020 2020 2020 * lay: \n 0001d1d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d1e0: 2020 2020 2020 2020 2020 2053 7065 6369 Speci\n-0001d1f0: 616c 206f 626a 6563 7473 2e20 2020 2020 al objects. \n-0001d200: 2028 6c69 6e65 2034 3829 0a2a 206c 6179 (line 48).* lay\n-0001d210: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+0001d1e0: 2020 2020 2020 2020 2053 7065 6369 616c Special\n+0001d1f0: 206f 626a 6563 7473 2e20 2020 2020 2028 objects. (\n+0001d200: 6c69 6e65 2034 3829 0a2a 206c 6179 203c line 48).* lay <\n+0001d210: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n 0001d220: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d230: 2020 2020 5469 6b5a 2f50 4746 2075 7365 TikZ/PGF use\n-0001d240: 722d 6465 6669 6e65 6420 7374 796c 6573 r-defined styles\n-0001d250: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+0001d230: 2020 5469 6b5a 2f50 4746 2075 7365 722d TikZ/PGF user-\n+0001d240: 6465 6669 6e65 6420 7374 796c 6573 2e0a defined styles..\n+0001d250: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d260: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d270: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d280: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d290: 2028 6c69 6e65 2033 3629 0a2a 206c 6179 (line 36).* lay\n-0001d2a0: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+0001d280: 2020 2020 2020 2020 2020 2020 2020 2028 (\n+0001d290: 6c69 6e65 2033 3629 0a2a 206c 6179 203c line 36).* lay <\n+0001d2a0: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n 0001d2b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d2c0: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n-0001d2d0: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n-0001d2e0: 3236 290a 2a20 6c61 7920 3c33 3e3a 2020 26).* lay <3>: \n+0001d2c0: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n+0001d2d0: 6177 696e 672e 2020 286c 696e 6520 3236 awing. (line 26\n+0001d2e0: 290a 2a20 6c61 7920 3c33 3e3a 2020 2020 ).* lay <3>: \n 0001d2f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d300: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n-0001d310: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n-0001d320: 2e20 2028 6c69 6e65 2032 3629 0a2a 206c . (line 26).* l\n-0001d330: 6179 203c 343e 3a20 2020 2020 2020 2020 ay <4>: \n+0001d300: 2020 2020 2020 2020 2020 2041 2074 6563 A tec\n+0001d310: 686e 6963 616c 2064 7261 7769 6e67 2e20 hnical drawing. \n+0001d320: 2028 6c69 6e65 2032 3629 0a2a 206c 6179 (line 26).* lay\n+0001d330: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n 0001d340: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d350: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n-0001d360: 6c20 6472 6177 696e 672e 2020 286c 696e l drawing. (lin\n-0001d370: 6520 3935 290a 2a20 6c61 7920 3c35 3e3a e 95).* lay <5>:\n+0001d350: 2020 2020 4120 7465 6368 6e69 6361 6c20 A technical \n+0001d360: 6472 6177 696e 672e 2020 286c 696e 6520 drawing. (line \n+0001d370: 3935 290a 2a20 6c61 7920 3c35 3e3a 2020 95).* lay <5>: \n 0001d380: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d390: 2020 2020 2020 2020 2020 2020 2020 2049 I\n-0001d3a0: 6e74 6572 6e61 6c20 6f70 7469 6f6e 732e nternal options.\n-0001d3b0: 2020 2020 2028 6c69 6e65 2020 3729 0a2a (line 7).*\n-0001d3c0: 206c 6179 203c 363e 3a20 2020 2020 2020 lay <6>: \n+0001d390: 2020 2020 2020 2020 2020 2020 2049 6e74 Int\n+0001d3a0: 6572 6e61 6c20 6f70 7469 6f6e 732e 2020 ernal options. \n+0001d3b0: 2020 2028 6c69 6e65 2020 3729 0a2a 206c (line 7).* l\n+0001d3c0: 6179 203c 363e 3a20 2020 2020 2020 2020 ay <6>: \n 0001d3d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d3e0: 2020 2020 2020 2020 5370 6563 6961 6c73 Specials\n-0001d3f0: 2e20 2020 2020 2020 2020 2020 2020 286c . (l\n-0001d400: 696e 6520 3432 290a 2a20 6c61 7920 3c37 ine 42).* lay <7\n-0001d410: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001d420: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d430: 2047 6c6f 6261 6c20 6f70 7469 6f6e 732e Global options.\n-0001d440: 2020 2020 2020 2028 6c69 6e65 2031 3329 (line 13)\n-0001d450: 0a2a 206c 696e 653a 2020 2020 2020 2020 .* line: \n+0001d3e0: 2020 2020 2020 5370 6563 6961 6c73 2e20 Specials. \n+0001d3f0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+0001d400: 6520 3432 290a 2a20 6c61 7920 3c37 3e3a e 42).* lay <7>:\n+0001d410: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d420: 2020 2020 2020 2020 2020 2020 2020 2047 G\n+0001d430: 6c6f 6261 6c20 6f70 7469 6f6e 732e 2020 lobal options. \n+0001d440: 2020 2020 2028 6c69 6e65 2031 3329 0a2a (line 13).*\n+0001d450: 206c 696e 653a 2020 2020 2020 2020 2020 line: \n 0001d460: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d470: 2020 2020 2020 2020 2020 4472 6177 696e Drawin\n-0001d480: 6720 6f70 7469 6f6e 732e 2020 2020 2020 g options. \n-0001d490: 286c 696e 6520 2037 290a 2a20 6c69 6e65 (line 7).* line\n-0001d4a0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+0001d470: 2020 2020 2020 2020 4472 6177 696e 6720 Drawing \n+0001d480: 6f70 7469 6f6e 732e 2020 2020 2020 286c options. (l\n+0001d490: 696e 6520 2037 290a 2a20 6c69 6e65 203c ine 7).* line <\n+0001d4a0: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n 0001d4b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d4c0: 2020 204f 626a 6563 7420 7472 616e 7366 Object transf\n-0001d4d0: 6f72 6d73 2e20 2020 2028 6c69 6e65 2031 orms. (line 1\n-0001d4e0: 3029 0a2a 206c 696e 6520 3c32 3e3a 2020 0).* line <2>: \n+0001d4c0: 204f 626a 6563 7420 7472 616e 7366 6f72 Object transfor\n+0001d4d0: 6d73 2e20 2020 2028 6c69 6e65 2031 3029 ms. (line 10)\n+0001d4e0: 0a2a 206c 696e 6520 3c32 3e3a 2020 2020 .* line <2>: \n 0001d4f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d500: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-0001d510: 6c69 6e65 2073 7765 6570 7320 7769 7468 line sweeps with\n-0001d520: 2063 6c6f 7375 7265 2e0a 2020 2020 2020 closure.. \n+0001d500: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n+0001d510: 6e65 2073 7765 6570 7320 7769 7468 2063 ne sweeps with c\n+0001d520: 6c6f 7375 7265 2e0a 2020 2020 2020 2020 losure.. \n 0001d530: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d540: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d550: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d560: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n-0001d570: 3029 0a2a 206c 696e 6520 3c33 3e3a 2020 0).* line <3>: \n+0001d560: 2020 2020 2020 2028 6c69 6e65 2031 3029 (line 10)\n+0001d570: 0a2a 206c 696e 6520 3c33 3e3a 2020 2020 .* line <3>: \n 0001d580: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d590: 2020 2020 2020 2020 2020 2020 4166 6669 Affi\n-0001d5a0: 6e65 2061 7269 7468 6d65 7469 632e 2020 ne arithmetic. \n-0001d5b0: 2020 286c 696e 6520 3131 290a 2a20 6c69 (line 11).* li\n-0001d5c0: 6e65 203c 343e 3a20 2020 2020 2020 2020 ne <4>: \n+0001d590: 2020 2020 2020 2020 2020 4166 6669 6e65 Affine\n+0001d5a0: 2061 7269 7468 6d65 7469 632e 2020 2020 arithmetic. \n+0001d5b0: 286c 696e 6520 3131 290a 2a20 6c69 6e65 (line 11).* line\n+0001d5c0: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n 0001d5d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d5e0: 2020 2020 204c 696e 6573 2e20 2020 2020 Lines. \n-0001d5f0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001d600: 2020 3629 0a2a 206c 696e 6520 3c35 3e3a 6).* line <5>:\n+0001d5e0: 2020 204c 696e 6573 2e20 2020 2020 2020 Lines. \n+0001d5f0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+0001d600: 3629 0a2a 206c 696e 6520 3c35 3e3a 2020 6).* line <5>: \n 0001d610: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d620: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-0001d630: 6570 7420 626c 6f63 6b73 2e20 2020 2020 ept blocks. \n-0001d640: 2020 2020 286c 696e 6520 2037 290a 2a20 (line 7).* \n-0001d650: 6c69 6e65 203c 363e 3a20 2020 2020 2020 line <6>: \n+0001d620: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+0001d630: 7420 626c 6f63 6b73 2e20 2020 2020 2020 t blocks. \n+0001d640: 2020 286c 696e 6520 2037 290a 2a20 6c69 (line 7).* li\n+0001d650: 6e65 203c 363e 3a20 2020 2020 2020 2020 ne <6>: \n 0001d660: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d670: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n-0001d680: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001d690: 6e65 2036 3929 0a2a 206c 696e 6520 3c37 ne 69).* line <7\n-0001d6a0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001d6b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d6c0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001d6d0: 696e 672e 2020 286c 696e 6520 3230 290a ing. 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(line 41).\n+0001d770: 2a20 6c69 6e65 203c 3130 3e3a 2020 2020 * line <10>: \n 0001d780: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d790: 2020 2020 2020 2020 2020 2041 2074 6563 A tec\n-0001d7a0: 686e 6963 616c 2064 7261 7769 6e67 2e20 hnical drawing. \n-0001d7b0: 2028 6c69 6e65 2036 3829 0a2a 206c 696e (line 68).* lin\n-0001d7c0: 6520 3c31 313e 3a20 2020 2020 2020 2020 e <11>: \n+0001d790: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n+0001d7a0: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n+0001d7b0: 6c69 6e65 2036 3829 0a2a 206c 696e 6520 line 68).* line \n+0001d7c0: 3c31 313e 3a20 2020 2020 2020 2020 2020 <11>: \n 0001d7d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d7e0: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n-0001d7f0: 616c 206d 6f64 656c 2e20 286c 696e 6520 al model. (line \n-0001d800: 3130 290a 2a20 6c69 6e65 2073 7479 6c65 10).* line style\n-0001d810: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001d820: 2020 2020 2020 2020 2020 2020 2054 696b Tik\n-0001d830: 5a2f 5047 4620 7573 6572 2d64 6566 696e Z/PGF user-defin\n-0001d840: 6564 2073 7479 6c65 732e 0a20 2020 2020 ed styles.. \n+0001d7e0: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n+0001d7f0: 206d 6f64 656c 2e20 286c 696e 6520 3130 model. (line 10\n+0001d800: 290a 2a20 6c69 6e65 2073 7479 6c65 3a20 ).* line style: \n+0001d810: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001d820: 2020 2020 2020 2020 2020 2054 696b 5a2f TikZ/\n+0001d830: 5047 4620 7573 6572 2d64 6566 696e 6564 PGF user-defined\n+0001d840: 2073 7479 6c65 732e 0a20 2020 2020 2020 styles.. \n 0001d850: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d860: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001d870: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d880: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001d890: 3235 290a 2a20 6c69 6e65 636f 6c6f 723a 25).* linecolor:\n+0001d880: 2020 2020 2020 2020 286c 696e 6520 3235 (line 25\n+0001d890: 290a 2a20 6c69 6e65 636f 6c6f 723a 2020 ).* linecolor: \n 0001d8a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d8b0: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n-0001d8c0: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n-0001d8d0: 2020 2028 6c69 6e65 2031 3029 0a2a 206c (line 10).* l\n-0001d8e0: 696e 6563 6f6c 6f72 203c 313e 3a20 2020 inecolor <1>: \n+0001d8b0: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n+0001d8c0: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n+0001d8d0: 2028 6c69 6e65 2031 3029 0a2a 206c 696e (line 10).* lin\n+0001d8e0: 6563 6f6c 6f72 203c 313e 3a20 2020 2020 ecolor <1>: \n 0001d8f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d900: 2020 2020 2020 4672 616d 652e 2020 2020 Frame. \n-0001d910: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-0001d920: 6520 3130 290a 2a20 6c69 6e65 636f 6c6f e 10).* linecolo\n-0001d930: 7220 3c32 3e3a 2020 2020 2020 2020 2020 r <2>: \n-0001d940: 2020 2020 2020 2020 2020 2020 2020 204f O\n-0001d950: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n-0001d960: 2020 2020 2028 6c69 6e65 2036 3929 0a2a (line 69).*\n-0001d970: 206c 696e 6573 7479 6c65 3a20 2020 2020 linestyle: \n+0001d900: 2020 2020 4672 616d 652e 2020 2020 2020 Frame. \n+0001d910: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001d920: 3130 290a 2a20 6c69 6e65 636f 6c6f 7220 10).* linecolor \n+0001d930: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n+0001d940: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n+0001d950: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n+0001d960: 2020 2028 6c69 6e65 2036 3929 0a2a 206c (line 69).* l\n+0001d970: 696e 6573 7479 6c65 3a20 2020 2020 2020 inestyle: \n 0001d980: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d990: 2020 2020 2020 2020 4672 616d 652e 2020 Frame. \n-0001d9a0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n-0001d9b0: 696e 6520 3130 290a 2a20 6c69 6e65 7374 ine 10).* linest\n-0001d9c0: 796c 6520 3c31 3e3a 2020 2020 2020 2020 yle <1>: \n-0001d9d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001d9e0: 204f 7665 7276 6965 772e 2020 2020 2020 Overview. \n-0001d9f0: 2020 2020 2020 2028 6c69 6e65 2036 3929 (line 69)\n-0001da00: 0a2a 206c 696e 6573 7479 6c65 203c 323e .* linestyle <2>\n-0001da10: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001da20: 2020 2020 2020 2020 2020 4120 7465 6368 A tech\n-0001da30: 6e69 6361 6c20 6472 6177 696e 672e 2020 nical drawing. \n-0001da40: 286c 696e 6520 3236 290a 2a20 6c69 6e65 (line 26).* line\n-0001da50: 7374 796c 6520 3c33 3e3a 2020 2020 2020 style <3>: \n+0001d990: 2020 2020 2020 4672 616d 652e 2020 2020 Frame. \n+0001d9a0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+0001d9b0: 6520 3130 290a 2a20 6c69 6e65 7374 796c e 10).* linestyl\n+0001d9c0: 6520 3c31 3e3a 2020 2020 2020 2020 2020 e <1>: \n+0001d9d0: 2020 2020 2020 2020 2020 2020 2020 204f O\n+0001d9e0: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n+0001d9f0: 2020 2020 2028 6c69 6e65 2036 3929 0a2a (line 69).*\n+0001da00: 206c 696e 6573 7479 6c65 203c 323e 3a20 linestyle <2>: \n+0001da10: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001da20: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n+0001da30: 6361 6c20 6472 6177 696e 672e 2020 286c cal drawing. (l\n+0001da40: 696e 6520 3236 290a 2a20 6c69 6e65 7374 ine 26).* linest\n+0001da50: 796c 6520 3c33 3e3a 2020 2020 2020 2020 yle <3>: \n 0001da60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001da70: 2020 2042 7567 7320 616e 6420 616e 6f6d Bugs and anom\n-0001da80: 616c 6965 732e 2020 2028 6c69 6e65 2020 alies. (line \n-0001da90: 3729 0a2a 206c 696e 6577 6964 7468 3a20 7).* linewidth: \n+0001da70: 2042 7567 7320 616e 6420 616e 6f6d 616c Bugs and anomal\n+0001da80: 6965 732e 2020 2028 6c69 6e65 2020 3729 ies. (line 7)\n+0001da90: 0a2a 206c 696e 6577 6964 7468 3a20 2020 .* linewidth: \n 0001daa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dab0: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-0001dac0: 6c69 6e65 2073 7765 6570 732e 2020 2020 line sweeps. \n-0001dad0: 2020 286c 696e 6520 2039 290a 2a20 6c69 (line 9).* li\n-0001dae0: 6e65 7769 6474 6820 3c31 3e3a 2020 2020 newidth <1>: \n+0001dab0: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n+0001dac0: 6e65 2073 7765 6570 732e 2020 2020 2020 ne sweeps. \n+0001dad0: 286c 696e 6520 2039 290a 2a20 6c69 6e65 (line 9).* line\n+0001dae0: 7769 6474 6820 3c31 3e3a 2020 2020 2020 width <1>: \n 0001daf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001db00: 2020 2020 2046 7261 6d65 2e20 2020 2020 Frame. \n-0001db10: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001db20: 2031 3029 0a2a 206c 696e 6577 6964 7468 10).* linewidth\n-0001db30: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n-0001db40: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001db50: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001db60: 2020 2020 286c 696e 6520 3639 290a 2a20 (line 69).* \n-0001db70: 6c69 6e65 7769 6474 6820 3c33 3e3a 2020 linewidth <3>: \n+0001db00: 2020 2046 7261 6d65 2e20 2020 2020 2020 Frame. \n+0001db10: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n+0001db20: 3029 0a2a 206c 696e 6577 6964 7468 203c 0).* linewidth <\n+0001db30: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n+0001db40: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n+0001db50: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n+0001db60: 2020 286c 696e 6520 3639 290a 2a20 6c69 (line 69).* li\n+0001db70: 6e65 7769 6474 6820 3c33 3e3a 2020 2020 newidth <3>: \n 0001db80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001db90: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n-0001dba0: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n-0001dbb0: 6e65 2032 3629 0a2a 206f 7061 6369 7479 ne 26).* opacity\n-0001dbc0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001dbd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dbe0: 5472 616e 7370 6172 656e 6379 2e20 2020 Transparency. \n-0001dbf0: 2020 2020 2020 286c 696e 6520 3130 290a (line 10).\n-0001dc00: 2a20 7065 7273 7065 6374 6976 653a 2020 * perspective: \n+0001db90: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n+0001dba0: 2064 7261 7769 6e67 2e20 2028 6c69 6e65 drawing. (line\n+0001dbb0: 2032 3629 0a2a 206f 7061 6369 7479 3a20 26).* opacity: \n+0001dbc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001dbd0: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n+0001dbe0: 616e 7370 6172 656e 6379 2e20 2020 2020 ansparency. \n+0001dbf0: 2020 2020 286c 696e 6520 3130 290a 2a20 (line 10).* \n+0001dc00: 7065 7273 7065 6374 6976 653a 2020 2020 perspective: \n 0001dc10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dc20: 2020 2020 2020 2020 2054 7261 6e73 666f Transfo\n-0001dc30: 726d 206c 6974 6572 616c 732e 2020 2028 rm literals. (\n-0001dc40: 6c69 6e65 2032 3129 0a2a 2070 6963 7475 line 21).* pictu\n-0001dc50: 7265 626f 783a 2020 2020 2020 2020 2020 rebox: \n+0001dc20: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n+0001dc30: 206c 6974 6572 616c 732e 2020 2028 6c69 literals. (li\n+0001dc40: 6e65 2032 3129 0a2a 2070 6963 7475 7265 ne 21).* picture\n+0001dc50: 626f 783a 2020 2020 2020 2020 2020 2020 box: \n 0001dc60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dc70: 2020 5069 6374 7572 6520 626f 782e 2020 Picture box. \n-0001dc80: 2020 2020 2020 2020 286c 696e 6520 2036 (line 6\n-0001dc90: 290a 2a20 706f 696e 7420 6c69 7374 3a20 ).* point list: \n+0001dc70: 5069 6374 7572 6520 626f 782e 2020 2020 Picture box. \n+0001dc80: 2020 2020 2020 286c 696e 6520 2036 290a (line 6).\n+0001dc90: 2a20 706f 696e 7420 6c69 7374 3a20 2020 * point list: \n 0001dca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dcb0: 2020 2020 2020 2020 2020 2049 6e74 6572 Inter\n-0001dcc0: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020 nal options. \n-0001dcd0: 2028 6c69 6e65 2032 3429 0a2a 2070 6f6c (line 24).* pol\n-0001dce0: 7967 6f6e 3a20 2020 2020 2020 2020 2020 ygon: \n+0001dcb0: 2020 2020 2020 2020 2049 6e74 6572 6e61 Interna\n+0001dcc0: 6c20 6f70 7469 6f6e 732e 2020 2020 2028 l options. (\n+0001dcd0: 6c69 6e65 2032 3429 0a2a 2070 6f6c 7967 line 24).* polyg\n+0001dce0: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n 0001dcf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dd00: 2020 2020 4865 6c6c 6f20 776f 726c 642e Hello world.\n-0001dd10: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001dd20: 3338 290a 2a20 706f 6c79 676f 6e20 3c31 38).* polygon <1\n-0001dd30: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001dd40: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n-0001dd50: 7769 6e67 2061 2073 6f6c 6964 2e20 2020 wing a solid. \n-0001dd60: 2020 2028 6c69 6e65 2020 3929 0a2a 2070 (line 9).* p\n-0001dd70: 6f6c 7967 6f6e 203c 323e 3a20 2020 2020 olygon <2>: \n+0001dd00: 2020 4865 6c6c 6f20 776f 726c 642e 2020 Hello world. \n+0001dd10: 2020 2020 2020 2020 286c 696e 6520 3338 (line 38\n+0001dd20: 290a 2a20 706f 6c79 676f 6e20 3c31 3e3a ).* polygon <1>:\n+0001dd30: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001dd40: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+0001dd50: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n+0001dd60: 2028 6c69 6e65 2020 3929 0a2a 2070 6f6c (line 9).* pol\n+0001dd70: 7967 6f6e 203c 323e 3a20 2020 2020 2020 ygon <2>: \n 0001dd80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dd90: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n-0001dda0: 6e73 666f 726d 732e 2020 2020 286c 696e nsforms. (lin\n-0001ddb0: 6520 3130 290a 2a20 706f 6c79 676f 6e20 e 10).* polygon \n-0001ddc0: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n-0001ddd0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001dde0: 6666 696e 6520 6172 6974 686d 6574 6963 ffine arithmetic\n-0001ddf0: 2e20 2020 2028 6c69 6e65 2031 3129 0a2a . (line 11).*\n-0001de00: 2070 6f6c 7967 6f6e 203c 343e 3a20 2020 polygon <4>: \n+0001dd90: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n+0001dda0: 666f 726d 732e 2020 2020 286c 696e 6520 forms. (line \n+0001ddb0: 3130 290a 2a20 706f 6c79 676f 6e20 3c33 10).* polygon <3\n+0001ddc0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+0001ddd0: 2020 2020 2020 2020 2020 2020 2041 6666 Aff\n+0001dde0: 696e 6520 6172 6974 686d 6574 6963 2e20 ine arithmetic. \n+0001ddf0: 2020 2028 6c69 6e65 2031 3129 0a2a 2070 (line 11).* p\n+0001de00: 6f6c 7967 6f6e 203c 343e 3a20 2020 2020 olygon <4>: \n 0001de10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001de20: 2020 2020 2020 2020 506f 6c79 676f 6e73 Polygons\n-0001de30: 2e20 2020 2020 2020 2020 2020 2020 286c . (l\n-0001de40: 696e 6520 2036 290a 2a20 706f 6c79 676f ine 6).* polygo\n-0001de50: 6e20 3c35 3e3a 2020 2020 2020 2020 2020 n <5>: \n-0001de60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001de70: 2053 7765 7074 2062 6c6f 636b 732e 2020 Swept blocks. \n-0001de80: 2020 2020 2020 2028 6c69 6e65 2020 3729 (line 7)\n-0001de90: 0a2a 2070 6f6c 7967 6f6e 203c 363e 3a20 .* polygon <6>: \n+0001de20: 2020 2020 2020 506f 6c79 676f 6e73 2e20 Polygons. \n+0001de30: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+0001de40: 6520 2036 290a 2a20 706f 6c79 676f 6e20 e 6).* polygon \n+0001de50: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n+0001de60: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+0001de70: 7765 7074 2062 6c6f 636b 732e 2020 2020 wept blocks. \n+0001de80: 2020 2020 2028 6c69 6e65 2020 3729 0a2a (line 7).*\n+0001de90: 2070 6f6c 7967 6f6e 203c 363e 3a20 2020 polygon <6>: \n 0001dea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001deb0: 2020 2020 2020 2020 2020 4f76 6572 7669 Overvi\n-0001dec0: 6577 2e20 2020 2020 2020 2020 2020 2020 ew. \n-0001ded0: 286c 696e 6520 3337 290a 2a20 7072 6f6a (line 37).* proj\n-0001dee0: 6563 743a 2020 2020 2020 2020 2020 2020 ect: \n+0001deb0: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n+0001dec0: 2e20 2020 2020 2020 2020 2020 2020 286c . (l\n+0001ded0: 696e 6520 3337 290a 2a20 7072 6f6a 6563 ine 37).* projec\n+0001dee0: 743a 2020 2020 2020 2020 2020 2020 2020 t: \n 0001def0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001df00: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n-0001df10: 6572 616c 732e 2020 2028 6c69 6e65 2031 erals. (line 1\n-0001df20: 3829 0a2a 2070 726f 6a65 6374 203c 313e 8).* project <1>\n-0001df30: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001df40: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n-0001df50: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-0001df60: 2020 286c 696e 6520 3139 290a 2a20 7072 (line 19).* pr\n-0001df70: 6f6a 6563 7420 3c32 3e3a 2020 2020 2020 oject <2>: \n+0001df00: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n+0001df10: 616c 732e 2020 2028 6c69 6e65 2031 3829 als. (line 18)\n+0001df20: 0a2a 2070 726f 6a65 6374 203c 313e 3a20 .* project <1>: \n+0001df30: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001df40: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+0001df50: 6f72 6d20 6c69 7465 7261 6c73 2e20 2020 orm literals. \n+0001df60: 286c 696e 6520 3139 290a 2a20 7072 6f6a (line 19).* proj\n+0001df70: 6563 7420 3c32 3e3a 2020 2020 2020 2020 ect <2>: \n 0001df80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001df90: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-0001dfa0: 6974 6572 616c 732e 2020 2028 6c69 6e65 iterals. (line\n-0001dfb0: 2034 3729 0a2a 2070 7374 7269 636b 733a 47).* pstricks:\n+0001df90: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+0001dfa0: 6572 616c 732e 2020 2028 6c69 6e65 2034 erals. (line 4\n+0001dfb0: 3729 0a2a 2070 7374 7269 636b 733a 2020 7).* pstricks: \n 0001dfc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001dfd0: 2020 2020 2020 2020 2020 2020 2020 4c61 La\n-0001dfe0: 6e67 7561 6765 2e20 2020 2020 2020 2020 nguage. \n-0001dff0: 2020 2020 286c 696e 6520 3130 290a 2a20 (line 10).* \n-0001e000: 7075 743a 2020 2020 2020 2020 2020 2020 put: \n+0001dfd0: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n+0001dfe0: 7561 6765 2e20 2020 2020 2020 2020 2020 uage. \n+0001dff0: 2020 286c 696e 6520 3130 290a 2a20 7075 (line 10).* pu\n+0001e000: 743a 2020 2020 2020 2020 2020 2020 2020 t: \n 0001e010: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e020: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n-0001e030: 616e 7366 6f72 6d73 2e20 2020 2028 6c69 ansforms. (li\n-0001e040: 6e65 2031 3029 0a2a 2070 7574 203c 313e ne 10).* put <1>\n-0001e050: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001e060: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e070: 4e65 7374 6564 2073 7765 6570 732e 2020 Nested sweeps. \n-0001e080: 2020 2020 2020 286c 696e 6520 3235 290a (line 25).\n-0001e090: 2a20 7075 7420 3c32 3e3a 2020 2020 2020 * put <2>: \n+0001e020: 2020 2020 204f 626a 6563 7420 7472 616e Object tran\n+0001e030: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65 sforms. (line\n+0001e040: 2031 3029 0a2a 2070 7574 203c 313e 3a20 10).* put <1>: \n+0001e050: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e060: 2020 2020 2020 2020 2020 2020 2020 4e65 Ne\n+0001e070: 7374 6564 2073 7765 6570 732e 2020 2020 sted sweeps. \n+0001e080: 2020 2020 286c 696e 6520 3235 290a 2a20 (line 25).* \n+0001e090: 7075 7420 3c32 3e3a 2020 2020 2020 2020 put <2>: \n 0001e0a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e0b0: 2020 2020 2020 2020 2050 7574 732e 2020 Puts. \n-0001e0c0: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-0001e0d0: 6c69 6e65 2020 3629 0a2a 2070 7574 203c line 6).* put <\n-0001e0e0: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n+0001e0b0: 2020 2020 2020 2050 7574 732e 2020 2020 Puts. \n+0001e0c0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+0001e0d0: 6e65 2020 3629 0a2a 2070 7574 203c 333e ne 6).* put <3>\n+0001e0e0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n 0001e0f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e100: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n-0001e110: 206d 6f64 656c 2e20 286c 696e 6520 3332 model. (line 32\n-0001e120: 290a 2a20 7265 7065 6174 3a20 2020 2020 ).* repeat: \n+0001e100: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n+0001e110: 6f64 656c 2e20 286c 696e 6520 3332 290a odel. (line 32).\n+0001e120: 2a20 7265 7065 6174 3a20 2020 2020 2020 * repeat: \n 0001e130: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e140: 2020 2020 2020 2020 2020 2052 6570 6561 Repea\n-0001e150: 7465 6420 6f62 6a65 6374 732e 2020 2020 ted objects. \n-0001e160: 2028 6c69 6e65 2020 3829 0a2a 2072 6570 (line 8).* rep\n-0001e170: 6561 7420 3c31 3e3a 2020 2020 2020 2020 eat <1>: \n+0001e140: 2020 2020 2020 2020 2052 6570 6561 7465 Repeate\n+0001e150: 6420 6f62 6a65 6374 732e 2020 2020 2028 d objects. (\n+0001e160: 6c69 6e65 2020 3829 0a2a 2072 6570 6561 line 8).* repea\n+0001e170: 7420 3c31 3e3a 2020 2020 2020 2020 2020 t <1>: \n 0001e180: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e190: 2020 2020 4e65 7374 6564 2073 7765 6570 Nested sweep\n-0001e1a0: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n-0001e1b0: 3235 290a 2a20 7265 7065 6174 203c 323e 25).* repeat <2>\n-0001e1c0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001e1d0: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n-0001e1e0: 796c 696e 6520 7377 6565 7073 2077 6974 yline sweeps wit\n-0001e1f0: 6820 636c 6f73 7572 652e 0a20 2020 2020 h closure.. \n+0001e190: 2020 4e65 7374 6564 2073 7765 6570 732e Nested sweeps.\n+0001e1a0: 2020 2020 2020 2020 286c 696e 6520 3235 (line 25\n+0001e1b0: 290a 2a20 7265 7065 6174 203c 323e 3a20 ).* repeat <2>: \n+0001e1c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e1d0: 2020 2020 2020 2020 2020 2050 6f6c 796c Polyl\n+0001e1e0: 696e 6520 7377 6565 7073 2077 6974 6820 ine sweeps with \n+0001e1f0: 636c 6f73 7572 652e 0a20 2020 2020 2020 closure.. \n 0001e200: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e210: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e220: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e230: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-0001e240: 3130 290a 2a20 7265 7065 6174 203c 333e 10).* repeat <3>\n-0001e250: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001e260: 2020 2020 2020 2020 2020 2020 2052 6570 Rep\n-0001e270: 6561 7473 2e20 2020 2020 2020 2020 2020 eats. \n-0001e280: 2020 2028 6c69 6e65 2020 3629 0a2a 2072 (line 6).* r\n-0001e290: 6570 6561 7420 3c34 3e3a 2020 2020 2020 epeat <4>: \n+0001e230: 2020 2020 2020 2020 286c 696e 6520 3130 (line 10\n+0001e240: 290a 2a20 7265 7065 6174 203c 333e 3a20 ).* repeat <3>: \n+0001e250: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e260: 2020 2020 2020 2020 2020 2052 6570 6561 Repea\n+0001e270: 7473 2e20 2020 2020 2020 2020 2020 2020 ts. \n+0001e280: 2028 6c69 6e65 2020 3629 0a2a 2072 6570 (line 6).* rep\n+0001e290: 6561 7420 3c34 3e3a 2020 2020 2020 2020 eat <4>: \n 0001e2a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e2b0: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n-0001e2c0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-0001e2d0: 6520 3537 290a 2a20 726f 7461 7465 3a20 e 57).* rotate: \n+0001e2b0: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n+0001e2c0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001e2d0: 3537 290a 2a20 726f 7461 7465 3a20 2020 57).* rotate: \n 0001e2e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e2f0: 2020 2020 2020 2020 2020 2020 2020 204f O\n-0001e300: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n-0001e310: 2e20 2020 2028 6c69 6e65 2031 3029 0a2a . (line 10).*\n-0001e320: 2072 6f74 6174 6520 3c31 3e3a 2020 2020 rotate <1>: \n+0001e2f0: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n+0001e300: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n+0001e310: 2020 2028 6c69 6e65 2031 3029 0a2a 2072 (line 10).* r\n+0001e320: 6f74 6174 6520 3c31 3e3a 2020 2020 2020 otate <1>: \n 0001e330: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e340: 2020 2020 2020 2020 4f62 6a65 6374 2074 Object t\n-0001e350: 7261 6e73 666f 726d 732e 2020 2020 286c ransforms. (l\n-0001e360: 696e 6520 3339 290a 2a20 726f 7461 7465 ine 39).* rotate\n-0001e370: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n-0001e380: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e390: 2052 6570 6561 7465 6420 6f62 6a65 6374 Repeated object\n-0001e3a0: 732e 2020 2020 2028 6c69 6e65 2020 3829 s. (line 8)\n-0001e3b0: 0a2a 2072 6f74 6174 6520 3c33 3e3a 2020 .* rotate <3>: \n+0001e340: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n+0001e350: 6e73 666f 726d 732e 2020 2020 286c 696e nsforms. (lin\n+0001e360: 6520 3339 290a 2a20 726f 7461 7465 203c e 39).* rotate <\n+0001e370: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n+0001e380: 2020 2020 2020 2020 2020 2020 2020 2052 R\n+0001e390: 6570 6561 7465 6420 6f62 6a65 6374 732e epeated objects.\n+0001e3a0: 2020 2020 2028 6c69 6e65 2020 3829 0a2a (line 8).*\n+0001e3b0: 2072 6f74 6174 6520 3c33 3e3a 2020 2020 rotate <3>: \n 0001e3c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e3d0: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n-0001e3e0: 6f62 6a65 6374 732e 2020 2020 2020 2020 objects. \n-0001e3f0: 286c 696e 6520 2038 290a 2a20 726f 7461 (line 8).* rota\n-0001e400: 7465 203c 343e 3a20 2020 2020 2020 2020 te <4>: \n+0001e3d0: 2020 2020 2020 2020 5377 6570 7420 6f62 Swept ob\n+0001e3e0: 6a65 6374 732e 2020 2020 2020 2020 286c jects. (l\n+0001e3f0: 696e 6520 2038 290a 2a20 726f 7461 7465 ine 8).* rotate\n+0001e400: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n 0001e410: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e420: 2020 2050 6f69 6e74 2073 7765 6570 732e Point sweeps.\n-0001e430: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n-0001e440: 3929 0a2a 2072 6f74 6174 6520 3c35 3e3a 9).* rotate <5>:\n+0001e420: 2050 6f69 6e74 2073 7765 6570 732e 2020 Point sweeps. \n+0001e430: 2020 2020 2020 2028 6c69 6e65 2031 3929 (line 19)\n+0001e440: 0a2a 2072 6f74 6174 6520 3c35 3e3a 2020 .* rotate <5>: \n 0001e450: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e460: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-0001e470: 6c69 6e65 2073 7765 6570 732e 2020 2020 line sweeps. \n-0001e480: 2020 286c 696e 6520 2039 290a 2a20 726f (line 9).* ro\n-0001e490: 7461 7465 203c 363e 3a20 2020 2020 2020 tate <6>: \n+0001e460: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n+0001e470: 6e65 2073 7765 6570 732e 2020 2020 2020 ne sweeps. \n+0001e480: 286c 696e 6520 2039 290a 2a20 726f 7461 (line 9).* rota\n+0001e490: 7465 203c 363e 3a20 2020 2020 2020 2020 te <6>: \n 0001e4a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e4b0: 2020 2020 204e 6573 7465 6420 7377 6565 Nested swee\n-0001e4c0: 7073 2e20 2020 2020 2020 2028 6c69 6e65 ps. (line\n-0001e4d0: 2020 3829 0a2a 2072 6f74 6174 6520 3c37 8).* rotate <7\n-0001e4e0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001e4f0: 2020 2020 2020 2020 2020 2020 2020 506f Po\n-0001e500: 6c79 6c69 6e65 2073 7765 6570 7320 7769 lyline sweeps wi\n-0001e510: 7468 2063 6c6f 7375 7265 2e0a 2020 2020 th closure.. \n+0001e4b0: 2020 204e 6573 7465 6420 7377 6565 7073 Nested sweeps\n+0001e4c0: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n+0001e4d0: 3829 0a2a 2072 6f74 6174 6520 3c37 3e3a 8).* rotate <7>:\n+0001e4e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e4f0: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n+0001e500: 6c69 6e65 2073 7765 6570 7320 7769 7468 line sweeps with\n+0001e510: 2063 6c6f 7375 7265 2e0a 2020 2020 2020 closure.. \n 0001e520: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e530: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e540: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e550: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001e560: 2031 3029 0a2a 2072 6f74 6174 6520 3c38 10).* rotate <8\n-0001e570: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001e580: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-0001e590: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-0001e5a0: 2e20 2020 286c 696e 6520 3130 290a 2a20 . (line 10).* \n-0001e5b0: 726f 7461 7465 203c 393e 3a20 2020 2020 rotate <9>: \n+0001e550: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n+0001e560: 3029 0a2a 2072 6f74 6174 6520 3c38 3e3a 0).* rotate <8>:\n+0001e570: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e580: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+0001e590: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+0001e5a0: 2020 286c 696e 6520 3130 290a 2a20 726f (line 10).* ro\n+0001e5b0: 7461 7465 203c 393e 3a20 2020 2020 2020 tate <9>: \n 0001e5c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e5d0: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n-0001e5e0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001e5f0: 6e65 2035 3729 0a2a 2072 6f74 6174 6520 ne 57).* rotate \n-0001e600: 3c31 303e 3a20 2020 2020 2020 2020 2020 <10>: \n-0001e610: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e620: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n-0001e630: 2020 2020 2020 286c 696e 6520 3639 290a (line 69).\n-0001e640: 2a20 726f 7461 7465 203c 3131 3e3a 2020 * rotate <11>: \n+0001e5d0: 2020 2020 204f 7665 7276 6965 772e 2020 Overview. \n+0001e5e0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001e5f0: 2035 3729 0a2a 2072 6f74 6174 6520 3c31 57).* rotate <1\n+0001e600: 303e 3a20 2020 2020 2020 2020 2020 2020 0>: \n+0001e610: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n+0001e620: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n+0001e630: 2020 2020 286c 696e 6520 3639 290a 2a20 (line 69).* \n+0001e640: 726f 7461 7465 203c 3131 3e3a 2020 2020 rotate <11>: \n 0001e650: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e660: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001e670: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001e680: 6c69 6e65 2031 3429 0a2a 2072 6f74 6174 line 14).* rotat\n-0001e690: 6520 3c31 323e 3a20 2020 2020 2020 2020 e <12>: \n+0001e660: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001e670: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001e680: 6e65 2031 3429 0a2a 2072 6f74 6174 6520 ne 14).* rotate \n+0001e690: 3c31 323e 3a20 2020 2020 2020 2020 2020 <12>: \n 0001e6a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e6b0: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n-0001e6c0: 206d 6f64 656c 2e20 286c 696e 6520 3130 model. (line 10\n-0001e6d0: 290a 2a20 726f 7461 7465 203c 3133 3e3a ).* rotate <13>:\n+0001e6b0: 4120 6869 6572 6172 6368 6963 616c 206d A hierarchical m\n+0001e6c0: 6f64 656c 2e20 286c 696e 6520 3130 290a odel. (line 10).\n+0001e6d0: 2a20 726f 7461 7465 203c 3133 3e3a 2020 * rotate <13>: \n 0001e6e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e6f0: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n-0001e700: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n-0001e710: 2028 6c69 6e65 2032 3329 0a2a 2072 6f74 (line 23).* rot\n-0001e720: 6174 6520 3c31 343e 3a20 2020 2020 2020 ate <14>: \n+0001e6f0: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n+0001e700: 7263 6869 6361 6c20 6d6f 6465 6c2e 2028 rchical model. (\n+0001e710: 6c69 6e65 2032 3329 0a2a 2072 6f74 6174 line 23).* rotat\n+0001e720: 6520 3c31 343e 3a20 2020 2020 2020 2020 e <14>: \n 0001e730: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e740: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n-0001e750: 616c 206d 6f64 656c 2e20 286c 696e 6520 al model. (line \n-0001e760: 3332 290a 2a20 7363 616c 653a 2020 2020 32).* scale: \n+0001e740: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n+0001e750: 206d 6f64 656c 2e20 286c 696e 6520 3332 model. (line 32\n+0001e760: 290a 2a20 7363 616c 653a 2020 2020 2020 ).* scale: \n 0001e770: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e780: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-0001e790: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n-0001e7a0: 2020 2028 6c69 6e65 2031 3629 0a2a 2073 (line 16).* s\n-0001e7b0: 6361 6c65 203c 313e 3a20 2020 2020 2020 cale <1>: \n+0001e780: 2020 2020 2020 2020 2020 2054 7261 6e73 Trans\n+0001e790: 666f 726d 206c 6974 6572 616c 732e 2020 form literals. \n+0001e7a0: 2028 6c69 6e65 2031 3629 0a2a 2073 6361 (line 16).* sca\n+0001e7b0: 6c65 203c 313e 3a20 2020 2020 2020 2020 le <1>: \n 0001e7c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e7d0: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n-0001e7e0: 6c69 7465 7261 6c73 2e20 2020 286c 696e literals. (lin\n-0001e7f0: 6520 3137 290a 2a20 7363 616c 6520 3c32 e 17).* scale <2\n-0001e800: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001e810: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001e820: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-0001e830: 6e67 2e20 2028 6c69 6e65 2034 3129 0a2a ng. (line 41).*\n-0001e840: 2073 6361 6c65 203c 333e 3a20 2020 2020 scale <3>: \n+0001e7d0: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n+0001e7e0: 7465 7261 6c73 2e20 2020 286c 696e 6520 terals. (line \n+0001e7f0: 3137 290a 2a20 7363 616c 6520 3c32 3e3a 17).* scale <2>:\n+0001e800: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001e810: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+0001e820: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+0001e830: 2e20 2028 6c69 6e65 2034 3129 0a2a 2073 . (line 41).* s\n+0001e840: 6361 6c65 203c 333e 3a20 2020 2020 2020 cale <3>: \n 0001e850: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e860: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n-0001e870: 6361 6c20 6472 6177 696e 672e 2020 286c cal drawing. (l\n-0001e880: 696e 6520 3638 290a 2a20 7363 616c 6520 ine 68).* scale \n-0001e890: 3c34 3e3a 2020 2020 2020 2020 2020 2020 <4>: \n-0001e8a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e8b0: 2041 2068 6965 7261 7263 6869 6361 6c20 A hierarchical \n-0001e8c0: 6d6f 6465 6c2e 2028 6c69 6e65 2033 3229 model. (line 32)\n-0001e8d0: 0a2a 2073 6574 3a20 2020 2020 2020 2020 .* set: \n+0001e860: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n+0001e870: 6c20 6472 6177 696e 672e 2020 286c 696e l drawing. (lin\n+0001e880: 6520 3638 290a 2a20 7363 616c 6520 3c34 e 68).* scale <4\n+0001e890: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+0001e8a0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n+0001e8b0: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n+0001e8c0: 6465 6c2e 2028 6c69 6e65 2033 3229 0a2a del. (line 32).*\n+0001e8d0: 2073 6574 3a20 2020 2020 2020 2020 2020 set: \n 0001e8e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e8f0: 2020 2020 2020 2020 2020 476c 6f62 616c Global\n-0001e900: 206f 7074 696f 6e73 2e20 2020 2020 2020 options. \n-0001e910: 286c 696e 6520 2036 290a 2a20 7369 6e3a (line 6).* sin:\n+0001e8f0: 2020 2020 2020 2020 476c 6f62 616c 206f Global o\n+0001e900: 7074 696f 6e73 2e20 2020 2020 2020 286c ptions. (l\n+0001e910: 696e 6520 2036 290a 2a20 7369 6e3a 2020 ine 6).* sin: \n 0001e920: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001e930: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e940: 2020 2055 6e61 7279 2066 6f72 6d73 2e20 Unary forms. \n-0001e950: 2020 2020 2020 2020 2028 6c69 6e65 2031 (line 1\n-0001e960: 3529 0a2a 2073 7065 6369 616c 3a20 2020 5).* special: \n+0001e940: 2055 6e61 7279 2066 6f72 6d73 2e20 2020 Unary forms. \n+0001e950: 2020 2020 2020 2028 6c69 6e65 2031 3529 (line 15)\n+0001e960: 0a2a 2073 7065 6369 616c 3a20 2020 2020 .* special: \n 0001e970: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e980: 2020 2020 2020 2020 2020 2020 5370 6563 Spec\n-0001e990: 6961 6c20 6f62 6a65 6374 732e 2020 2020 ial objects. \n-0001e9a0: 2020 286c 696e 6520 2036 290a 2a20 7370 (line 6).* sp\n-0001e9b0: 6563 6961 6c20 3c31 3e3a 2020 2020 2020 ecial <1>: \n+0001e980: 2020 2020 2020 2020 2020 5370 6563 6961 Specia\n+0001e990: 6c20 6f62 6a65 6374 732e 2020 2020 2020 l objects. \n+0001e9a0: 286c 696e 6520 2036 290a 2a20 7370 6563 (line 6).* spec\n+0001e9b0: 6961 6c20 3c31 3e3a 2020 2020 2020 2020 ial <1>: \n 0001e9c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001e9d0: 2020 2020 2053 7065 6369 616c 732e 2020 Specials. \n-0001e9e0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001e9f0: 2020 3629 0a2a 2073 7065 6369 616c 203c 6).* special <\n-0001ea00: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n-0001ea10: 2020 2020 2020 2020 2020 2020 2020 4f76 Ov\n-0001ea20: 6572 7669 6577 2e20 2020 2020 2020 2020 erview. \n-0001ea30: 2020 2020 286c 696e 6520 3639 290a 2a20 (line 69).* \n-0001ea40: 7370 6563 6961 6c20 3c33 3e3a 2020 2020 special <3>: \n+0001e9d0: 2020 2053 7065 6369 616c 732e 2020 2020 Specials. \n+0001e9e0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+0001e9f0: 3629 0a2a 2073 7065 6369 616c 203c 323e 6).* special <2>\n+0001ea00: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001ea10: 2020 2020 2020 2020 2020 2020 4f76 6572 Over\n+0001ea20: 7669 6577 2e20 2020 2020 2020 2020 2020 view. \n+0001ea30: 2020 286c 696e 6520 3639 290a 2a20 7370 (line 69).* sp\n+0001ea40: 6563 6961 6c20 3c33 3e3a 2020 2020 2020 ecial <3>: \n 0001ea50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ea60: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n-0001ea70: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n-0001ea80: 6e65 2032 3629 0a2a 2073 7065 6369 616c ne 26).* special\n-0001ea90: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n-0001eaa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eab0: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n-0001eac0: 696e 672e 2020 286c 696e 6520 3431 290a ing. (line 41).\n-0001ead0: 2a20 7370 6563 6961 6c20 3c35 3e3a 2020 * special <5>: \n+0001ea60: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n+0001ea70: 2064 7261 7769 6e67 2e20 2028 6c69 6e65 drawing. (line\n+0001ea80: 2032 3629 0a2a 2073 7065 6369 616c 203c 26).* special <\n+0001ea90: 343e 3a20 2020 2020 2020 2020 2020 2020 4>: \n+0001eaa0: 2020 2020 2020 2020 2020 2020 2020 4120 A \n+0001eab0: 7465 6368 6e69 6361 6c20 6472 6177 696e technical drawin\n+0001eac0: 672e 2020 286c 696e 6520 3431 290a 2a20 g. (line 41).* \n+0001ead0: 7370 6563 6961 6c20 3c35 3e3a 2020 2020 special <5>: \n 0001eae0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eaf0: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-0001eb00: 6963 616c 2064 7261 7769 6e67 2e20 2028 ical drawing. (\n-0001eb10: 6c69 6e65 2036 3829 0a2a 2073 7065 6369 line 68).* speci\n-0001eb20: 616c 203c 363e 3a20 2020 2020 2020 2020 al <6>: \n+0001eaf0: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+0001eb00: 616c 2064 7261 7769 6e67 2e20 2028 6c69 al drawing. (li\n+0001eb10: 6e65 2036 3829 0a2a 2073 7065 6369 616c ne 68).* special\n+0001eb20: 203c 363e 3a20 2020 2020 2020 2020 2020 <6>: \n 0001eb30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eb40: 2020 4120 7465 6368 6e69 6361 6c20 6472 A technical dr\n-0001eb50: 6177 696e 672e 2020 286c 696e 6520 3935 awing. (line 95\n-0001eb60: 290a 2a20 7370 6c69 743a 2020 2020 2020 ).* split: \n+0001eb40: 4120 7465 6368 6e69 6361 6c20 6472 6177 A technical draw\n+0001eb50: 696e 672e 2020 286c 696e 6520 3935 290a ing. (line 95).\n+0001eb60: 2a20 7370 6c69 743a 2020 2020 2020 2020 * split: \n 0001eb70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eb80: 2020 2020 2020 2020 2020 2049 6e74 6572 Inter\n-0001eb90: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020 nal options. \n-0001eba0: 2028 6c69 6e65 2020 3729 0a2a 2073 706c (line 7).* spl\n-0001ebb0: 6974 203c 313e 3a20 2020 2020 2020 2020 it <1>: \n+0001eb80: 2020 2020 2020 2020 2049 6e74 6572 6e61 Interna\n+0001eb90: 6c20 6f70 7469 6f6e 732e 2020 2020 2028 l options. (\n+0001eba0: 6c69 6e65 2020 3729 0a2a 2073 706c 6974 line 7).* split\n+0001ebb0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n 0001ebc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ebd0: 2020 2020 476c 6f62 616c 206f 7074 696f Global optio\n-0001ebe0: 6e73 2e20 2020 2020 2020 286c 696e 6520 ns. (line \n-0001ebf0: 3133 290a 2a20 7371 7274 3a20 2020 2020 13).* sqrt: \n+0001ebd0: 2020 476c 6f62 616c 206f 7074 696f 6e73 Global options\n+0001ebe0: 2e20 2020 2020 2020 286c 696e 6520 3133 . (line 13\n+0001ebf0: 290a 2a20 7371 7274 3a20 2020 2020 2020 ).* sqrt: \n 0001ec00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ec10: 2020 2020 2020 2020 2020 2020 2055 6e61 Una\n-0001ec20: 7279 2066 6f72 6d73 2e20 2020 2020 2020 ry forms. \n-0001ec30: 2020 2028 6c69 6e65 2031 3429 0a2a 2073 (line 14).* s\n-0001ec40: 7765 6570 3a20 2020 2020 2020 2020 2020 weep: \n+0001ec10: 2020 2020 2020 2020 2020 2055 6e61 7279 Unary\n+0001ec20: 2066 6f72 6d73 2e20 2020 2020 2020 2020 forms. \n+0001ec30: 2028 6c69 6e65 2031 3429 0a2a 2073 7765 (line 14).* swe\n+0001ec40: 6570 3a20 2020 2020 2020 2020 2020 2020 ep: \n 0001ec50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ec60: 2020 2020 2020 5377 6570 7420 6f62 6a65 Swept obje\n-0001ec70: 6374 732e 2020 2020 2020 2020 286c 696e cts. (lin\n-0001ec80: 6520 2038 290a 2a20 7377 6565 7020 3c31 e 8).* sweep <1\n-0001ec90: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001eca0: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-0001ecb0: 6f69 6e74 2073 7765 6570 732e 2020 2020 oint sweeps. \n-0001ecc0: 2020 2020 2028 6c69 6e65 2031 3929 0a2a (line 19).*\n-0001ecd0: 2073 7765 6570 203c 323e 3a20 2020 2020 sweep <2>: \n+0001ec60: 2020 2020 5377 6570 7420 6f62 6a65 6374 Swept object\n+0001ec70: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n+0001ec80: 2038 290a 2a20 7377 6565 7020 3c31 3e3a 8).* sweep <1>:\n+0001ec90: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001eca0: 2020 2020 2020 2020 2020 2020 2050 6f69 Poi\n+0001ecb0: 6e74 2073 7765 6570 732e 2020 2020 2020 nt sweeps. \n+0001ecc0: 2020 2028 6c69 6e65 2031 3929 0a2a 2073 (line 19).* s\n+0001ecd0: 7765 6570 203c 323e 3a20 2020 2020 2020 weep <2>: \n 0001ece0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ecf0: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n-0001ed00: 2073 7765 6570 732e 2020 2020 2020 286c sweeps. (l\n-0001ed10: 696e 6520 2039 290a 2a20 7377 6565 7020 ine 9).* sweep \n-0001ed20: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n-0001ed30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ed40: 204e 6573 7465 6420 7377 6565 7073 2e20 Nested sweeps. \n-0001ed50: 2020 2020 2020 2028 6c69 6e65 2020 3829 (line 8)\n-0001ed60: 0a2a 2073 7765 6570 203c 343e 3a20 2020 .* sweep <4>: \n+0001ecf0: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n+0001ed00: 7765 6570 732e 2020 2020 2020 286c 696e weeps. (lin\n+0001ed10: 6520 2039 290a 2a20 7377 6565 7020 3c33 e 9).* sweep <3\n+0001ed20: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+0001ed30: 2020 2020 2020 2020 2020 2020 2020 204e N\n+0001ed40: 6573 7465 6420 7377 6565 7073 2e20 2020 ested sweeps. \n+0001ed50: 2020 2020 2028 6c69 6e65 2020 3829 0a2a (line 8).*\n+0001ed60: 2073 7765 6570 203c 343e 3a20 2020 2020 sweep <4>: \n 0001ed70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ed80: 2020 2020 2020 2020 2020 4e65 7374 6564 Nested\n-0001ed90: 2073 7765 6570 732e 2020 2020 2020 2020 sweeps. \n-0001eda0: 286c 696e 6520 3232 290a 2a20 7377 6565 (line 22).* swee\n-0001edb0: 7020 3c35 3e3a 2020 2020 2020 2020 2020 p <5>: \n+0001ed80: 2020 2020 2020 2020 4e65 7374 6564 2073 Nested s\n+0001ed90: 7765 6570 732e 2020 2020 2020 2020 286c weeps. (l\n+0001eda0: 696e 6520 3232 290a 2a20 7377 6565 7020 ine 22).* sweep \n+0001edb0: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n 0001edc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001edd0: 2020 2050 6f6c 796c 696e 6520 7377 6565 Polyline swee\n-0001ede0: 7073 2077 6974 6820 636c 6f73 7572 652e ps with closure.\n-0001edf0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+0001edd0: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n+0001ede0: 2077 6974 6820 636c 6f73 7572 652e 0a20 with closure.. \n+0001edf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ee00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001ee10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ee20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ee30: 286c 696e 6520 3130 290a 2a20 7377 6565 (line 10).* swee\n-0001ee40: 7020 3c36 3e3a 2020 2020 2020 2020 2020 p <6>: \n+0001ee20: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001ee30: 696e 6520 3130 290a 2a20 7377 6565 7020 ine 10).* sweep \n+0001ee40: 3c36 3e3a 2020 2020 2020 2020 2020 2020 <6>: \n 0001ee50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ee60: 2020 2053 7765 6570 732e 2020 2020 2020 Sweeps. \n-0001ee70: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-0001ee80: 3629 0a2a 2073 7765 6570 203c 373e 3a20 6).* sweep <7>: \n+0001ee60: 2053 7765 6570 732e 2020 2020 2020 2020 Sweeps. \n+0001ee70: 2020 2020 2020 2028 6c69 6e65 2020 3629 (line 6)\n+0001ee80: 0a2a 2073 7765 6570 203c 373e 3a20 2020 .* sweep <7>: \n 0001ee90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eea0: 2020 2020 2020 2020 2020 2020 4120 7465 A te\n-0001eeb0: 6368 6e69 6361 6c20 6472 6177 696e 672e chnical drawing.\n-0001eec0: 2020 286c 696e 6520 3230 290a 2a20 7377 (line 20).* sw\n-0001eed0: 6565 7020 3c38 3e3a 2020 2020 2020 2020 eep <8>: \n+0001eea0: 2020 2020 2020 2020 2020 4120 7465 6368 A tech\n+0001eeb0: 6e69 6361 6c20 6472 6177 696e 672e 2020 nical drawing. \n+0001eec0: 286c 696e 6520 3230 290a 2a20 7377 6565 (line 20).* swee\n+0001eed0: 7020 3c38 3e3a 2020 2020 2020 2020 2020 p <8>: \n 0001eee0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001eef0: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n-0001ef00: 6361 6c20 6d6f 6465 6c2e 2028 6c69 6e65 cal model. (line\n-0001ef10: 2031 3029 0a2a 2073 7765 6570 203c 393e 10).* sweep <9>\n-0001ef20: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001ef30: 2020 2020 2020 2020 2020 2020 2020 4120 A \n-0001ef40: 6869 6572 6172 6368 6963 616c 206d 6f64 hierarchical mod\n-0001ef50: 656c 2e20 286c 696e 6520 3233 290a 2a20 el. (line 23).* \n-0001ef60: 7468 656e 3a20 2020 2020 2020 2020 2020 then: \n+0001eef0: 2020 2041 2068 6965 7261 7263 6869 6361 A hierarchica\n+0001ef00: 6c20 6d6f 6465 6c2e 2028 6c69 6e65 2031 l model. (line 1\n+0001ef10: 3029 0a2a 2073 7765 6570 203c 393e 3a20 0).* sweep <9>: \n+0001ef20: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001ef30: 2020 2020 2020 2020 2020 2020 4120 6869 A hi\n+0001ef40: 6572 6172 6368 6963 616c 206d 6f64 656c erarchical model\n+0001ef50: 2e20 286c 696e 6520 3233 290a 2a20 7468 . (line 23).* th\n+0001ef60: 656e 3a20 2020 2020 2020 2020 2020 2020 en: \n 0001ef70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ef80: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n-0001ef90: 616e 7366 6f72 6d73 2e20 2020 2028 6c69 ansforms. (li\n-0001efa0: 6e65 2031 3029 0a2a 2074 6865 6e20 3c31 ne 10).* then <1\n-0001efb0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001efc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001efd0: 506f 6c79 6c69 6e65 2073 7765 6570 7320 Polyline sweeps \n-0001efe0: 7769 7468 2063 6c6f 7375 7265 2e0a 2020 with closure.. \n+0001ef80: 2020 2020 204f 626a 6563 7420 7472 616e Object tran\n+0001ef90: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65 sforms. (line\n+0001efa0: 2031 3029 0a2a 2074 6865 6e20 3c31 3e3a 10).* then <1>:\n+0001efb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001efc0: 2020 2020 2020 2020 2020 2020 2020 506f Po\n+0001efd0: 6c79 6c69 6e65 2073 7765 6570 7320 7769 lyline sweeps wi\n+0001efe0: 7468 2063 6c6f 7375 7265 2e0a 2020 2020 th closure.. \n 0001eff0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f000: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f010: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f020: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-0001f030: 6e65 2031 3029 0a2a 2074 6865 6e20 3c32 ne 10).* then <2\n-0001f040: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001f050: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f060: 5477 6f2d 6f70 6572 616e 6420 2862 696e Two-operand (bin\n-0001f070: 6172 7929 2066 6f72 6d73 2e0a 2020 2020 ary) forms.. \n+0001f020: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+0001f030: 2031 3029 0a2a 2074 6865 6e20 3c32 3e3a 10).* then <2>:\n+0001f040: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f050: 2020 2020 2020 2020 2020 2020 2020 5477 Tw\n+0001f060: 6f2d 6f70 6572 616e 6420 2862 696e 6172 o-operand (binar\n+0001f070: 7929 2066 6f72 6d73 2e0a 2020 2020 2020 y) forms.. \n 0001f080: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f090: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f0a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f0b0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-0001f0c0: 2033 3629 0a2a 2074 6865 6e20 3c33 3e3a 36).* then <3>:\n+0001f0b0: 2020 2020 2020 2020 2028 6c69 6e65 2033 (line 3\n+0001f0c0: 3629 0a2a 2074 6865 6e20 3c33 3e3a 2020 6).* then <3>: \n 0001f0d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f0e0: 2020 2020 2020 2020 2020 2020 2020 5477 Tw\n-0001f0f0: 6f2d 6f70 6572 616e 6420 2862 696e 6172 o-operand (binar\n-0001f100: 7929 2066 6f72 6d73 2e0a 2020 2020 2020 y) forms.. \n+0001f0e0: 2020 2020 2020 2020 2020 2020 5477 6f2d Two-\n+0001f0f0: 6f70 6572 616e 6420 2862 696e 6172 7929 operand (binary)\n+0001f100: 2066 6f72 6d73 2e0a 2020 2020 2020 2020 forms.. \n 0001f110: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f120: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f130: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f140: 2020 2020 2020 2020 2028 6c69 6e65 2036 (line 6\n-0001f150: 3329 0a2a 2074 696b 7a3a 2020 2020 2020 3).* tikz: \n+0001f140: 2020 2020 2020 2028 6c69 6e65 2036 3329 (line 63)\n+0001f150: 0a2a 2074 696b 7a3a 2020 2020 2020 2020 .* tikz: \n 0001f160: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f170: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n-0001f180: 7561 6765 2e20 2020 2020 2020 2020 2020 uage. \n-0001f190: 2020 286c 696e 6520 3130 290a 2a20 7472 (line 10).* tr\n-0001f1a0: 616e 736c 6174 653a 2020 2020 2020 2020 anslate: \n+0001f170: 2020 2020 2020 2020 2020 4c61 6e67 7561 Langua\n+0001f180: 6765 2e20 2020 2020 2020 2020 2020 2020 ge. \n+0001f190: 286c 696e 6520 3130 290a 2a20 7472 616e (line 10).* tran\n+0001f1a0: 736c 6174 653a 2020 2020 2020 2020 2020 slate: \n 0001f1b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f1c0: 2020 2020 204f 626a 6563 7420 7472 616e Object tran\n-0001f1d0: 7366 6f72 6d73 2e20 2020 2028 6c69 6e65 sforms. (line\n-0001f1e0: 2031 3029 0a2a 2074 7261 6e73 6c61 7465 10).* translate\n-0001f1f0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-0001f200: 2020 2020 2020 2020 2020 2020 2020 4f62 Ob\n-0001f210: 6a65 6374 2074 7261 6e73 666f 726d 732e ject transforms.\n-0001f220: 2020 2020 286c 696e 6520 3437 290a 2a20 (line 47).* \n-0001f230: 7472 616e 736c 6174 6520 3c32 3e3a 2020 translate <2>: \n+0001f1c0: 2020 204f 626a 6563 7420 7472 616e 7366 Object transf\n+0001f1d0: 6f72 6d73 2e20 2020 2028 6c69 6e65 2031 orms. (line 1\n+0001f1e0: 3029 0a2a 2074 7261 6e73 6c61 7465 203c 0).* translate <\n+0001f1f0: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+0001f200: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n+0001f210: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n+0001f220: 2020 286c 696e 6520 3437 290a 2a20 7472 (line 47).* tr\n+0001f230: 616e 736c 6174 6520 3c32 3e3a 2020 2020 anslate <2>: \n 0001f240: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f250: 2020 2020 2020 2052 6570 6561 7465 6420 Repeated \n-0001f260: 6f62 6a65 6374 732e 2020 2020 2028 6c69 objects. (li\n-0001f270: 6e65 2020 3829 0a2a 2074 7261 6e73 6c61 ne 8).* transla\n-0001f280: 7465 203c 333e 3a20 2020 2020 2020 2020 te <3>: \n-0001f290: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f2a0: 506f 6c79 6c69 6e65 2073 7765 6570 732e Polyline sweeps.\n-0001f2b0: 2020 2020 2020 286c 696e 6520 2039 290a (line 9).\n-0001f2c0: 2a20 7472 616e 736c 6174 6520 3c34 3e3a * translate <4>:\n+0001f250: 2020 2020 2052 6570 6561 7465 6420 6f62 Repeated ob\n+0001f260: 6a65 6374 732e 2020 2020 2028 6c69 6e65 jects. (line\n+0001f270: 2020 3829 0a2a 2074 7261 6e73 6c61 7465 8).* translate\n+0001f280: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n+0001f290: 2020 2020 2020 2020 2020 2020 2020 506f Po\n+0001f2a0: 6c79 6c69 6e65 2073 7765 6570 732e 2020 lyline sweeps. \n+0001f2b0: 2020 2020 286c 696e 6520 2039 290a 2a20 (line 9).* \n+0001f2c0: 7472 616e 736c 6174 6520 3c34 3e3a 2020 translate <4>: \n 0001f2d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f2e0: 2020 2020 2020 2020 2050 6f6c 796c 696e Polylin\n-0001f2f0: 6520 7377 6565 7073 2077 6974 6820 636c e sweeps with cl\n-0001f300: 6f73 7572 652e 0a20 2020 2020 2020 2020 osure.. \n+0001f2e0: 2020 2020 2020 2050 6f6c 796c 696e 6520 Polyline \n+0001f2f0: 7377 6565 7073 2077 6974 6820 636c 6f73 sweeps with clos\n+0001f300: 7572 652e 0a20 2020 2020 2020 2020 2020 ure.. \n 0001f310: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f320: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f330: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f340: 2020 2020 2020 286c 696e 6520 3130 290a (line 10).\n-0001f350: 2a20 7472 616e 736c 6174 6520 3c35 3e3a * translate <5>:\n+0001f340: 2020 2020 286c 696e 6520 3130 290a 2a20 (line 10).* \n+0001f350: 7472 616e 736c 6174 6520 3c35 3e3a 2020 translate <5>: \n 0001f360: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f370: 2020 2020 2020 2020 2054 7261 6e73 666f Transfo\n-0001f380: 726d 206c 6974 6572 616c 732e 2020 2028 rm literals. (\n-0001f390: 6c69 6e65 2031 3529 0a2a 2074 7261 6e73 line 15).* trans\n-0001f3a0: 6c61 7465 203c 363e 3a20 2020 2020 2020 late <6>: \n+0001f370: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n+0001f380: 206c 6974 6572 616c 732e 2020 2028 6c69 literals. (li\n+0001f390: 6e65 2031 3529 0a2a 2074 7261 6e73 6c61 ne 15).* transla\n+0001f3a0: 7465 203c 363e 3a20 2020 2020 2020 2020 te <6>: \n 0001f3b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f3c0: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n-0001f3d0: 2020 2020 2020 2020 286c 696e 6520 3537 (line 57\n-0001f3e0: 290a 2a20 7472 616e 736c 6174 6520 3c37 ).* translate <7\n-0001f3f0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001f400: 2020 2020 2020 2020 2020 204f 7665 7276 Overv\n-0001f410: 6965 772e 2020 2020 2020 2020 2020 2020 iew. \n-0001f420: 2028 6c69 6e65 2036 3929 0a2a 2074 7261 (line 69).* tra\n-0001f430: 6e73 6c61 7465 203c 383e 3a20 2020 2020 nslate <8>: \n+0001f3c0: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n+0001f3d0: 2020 2020 2020 286c 696e 6520 3537 290a (line 57).\n+0001f3e0: 2a20 7472 616e 736c 6174 6520 3c37 3e3a * translate <7>:\n+0001f3f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f400: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n+0001f410: 772e 2020 2020 2020 2020 2020 2020 2028 w. (\n+0001f420: 6c69 6e65 2036 3929 0a2a 2074 7261 6e73 line 69).* trans\n+0001f430: 6c61 7465 203c 383e 3a20 2020 2020 2020 late <8>: \n 0001f440: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f450: 2020 2020 4120 6869 6572 6172 6368 6963 A hierarchic\n-0001f460: 616c 206d 6f64 656c 2e20 286c 696e 6520 al model. (line \n-0001f470: 3332 290a 2a20 7472 616e 7370 616c 7068 32).* transpalph\n-0001f480: 613a 2020 2020 2020 2020 2020 2020 2020 a: \n-0001f490: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-0001f4a0: 6e73 7061 7265 6e63 792e 2020 2020 2020 nsparency. \n-0001f4b0: 2020 2028 6c69 6e65 2031 3029 0a2a 2075 (line 10).* u\n-0001f4c0: 6e69 743a 2020 2020 2020 2020 2020 2020 nit: \n+0001f450: 2020 4120 6869 6572 6172 6368 6963 616c A hierarchical\n+0001f460: 206d 6f64 656c 2e20 286c 696e 6520 3332 model. (line 32\n+0001f470: 290a 2a20 7472 616e 7370 616c 7068 613a ).* transpalpha:\n+0001f480: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f490: 2020 2020 2020 2020 2020 2054 7261 6e73 Trans\n+0001f4a0: 7061 7265 6e63 792e 2020 2020 2020 2020 parency. \n+0001f4b0: 2028 6c69 6e65 2031 3029 0a2a 2075 6e69 (line 10).* uni\n+0001f4c0: 743a 2020 2020 2020 2020 2020 2020 2020 t: \n 0001f4d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f4e0: 2020 2020 2020 556e 6172 7920 666f 726d Unary form\n-0001f4f0: 732e 2020 2020 2020 2020 2020 286c 696e s. (lin\n-0001f500: 6520 3133 290a 2a20 756e 6974 203c 313e e 13).* unit <1>\n-0001f510: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001f520: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001f530: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-0001f540: 6e67 2e20 2028 6c69 6e65 2034 3129 0a2a ng. (line 41).*\n-0001f550: 2076 6965 773a 2020 2020 2020 2020 2020 view: \n+0001f4e0: 2020 2020 556e 6172 7920 666f 726d 732e Unary forms.\n+0001f4f0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001f500: 3133 290a 2a20 756e 6974 203c 313e 3a20 13).* unit <1>: \n+0001f510: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f520: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+0001f530: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+0001f540: 2e20 2028 6c69 6e65 2034 3129 0a2a 2076 . (line 41).* v\n+0001f550: 6965 773a 2020 2020 2020 2020 2020 2020 iew: \n 0001f560: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f570: 2020 2020 2020 2020 5472 616e 7366 6f72 Transfor\n-0001f580: 6d20 6c69 7465 7261 6c73 2e20 2020 286c m literals. (l\n-0001f590: 696e 6520 3235 290a 2a20 7669 6577 203c ine 25).* view <\n-0001f5a0: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-0001f5b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f5c0: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n-0001f5d0: 616c 732e 2020 2028 6c69 6e65 2033 3529 als. (line 35)\n-0001f5e0: 0a0a 1f0a 4669 6c65 3a20 736b 6574 6368 ....File: sketch\n-0001f5f0: 2e69 6e66 6f2c 2020 4e6f 6465 3a20 496e .info, Node: In\n-0001f600: 6465 782c 2020 5072 6576 3a20 496e 6465 dex, Prev: Inde\n-0001f610: 7820 6f66 2073 796e 7461 782c 2020 5570 x of syntax, Up\n-0001f620: 3a20 546f 700a 0a49 6e64 6578 206f 6620 : Top..Index of \n-0001f630: 636f 6e63 6570 7473 0a2a 2a2a 2a2a 2a2a concepts.*******\n-0001f640: 2a2a 2a2a 2a2a 2a2a 2a2a 0a0a 0008 5b69 **********....[i\n-0001f650: 6e64 6578 0008 5d0a 2a20 4d65 6e75 3a0a ndex..].* Menu:.\n-0001f660: 0a2a 2061 6666 696e 6520 6172 6974 686d .* affine arithm\n-0001f670: 6574 6963 3a20 2020 2020 2020 2020 2020 etic: \n-0001f680: 2020 2020 2020 2020 2020 4166 6669 6e65 Affine\n-0001f690: 2061 7269 7468 6d65 7469 632e 2020 2028 arithmetic. (\n-0001f6a0: 6c69 6e65 2020 2038 290a 2a20 6166 6669 line 8).* affi\n-0001f6b0: 6e65 2061 7269 7468 6d65 7469 6320 3c31 ne arithmetic <1\n-0001f6c0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-0001f6d0: 2020 2041 2074 6563 686e 6963 616c 2064 A technical d\n-0001f6e0: 7261 7769 6e67 2e20 286c 696e 6520 2034 rawing. (line 4\n-0001f6f0: 3029 0a2a 2061 6c74 6572 6e61 7469 7665 0).* alternative\n-0001f700: 732c 2064 6566 696e 6974 696f 6e3a 2020 s, definition: \n-0001f710: 2020 2020 2020 2020 2020 2020 466f 726d Form\n-0001f720: 7320 6f66 2064 6566 696e 6974 696f 6e73 s of definitions\n-0001f730: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+0001f570: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n+0001f580: 6c69 7465 7261 6c73 2e20 2020 286c 696e literals. (lin\n+0001f590: 6520 3235 290a 2a20 7669 6577 203c 313e e 25).* view <1>\n+0001f5a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001f5b0: 2020 2020 2020 2020 2020 2020 2020 2054 T\n+0001f5c0: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n+0001f5d0: 732e 2020 2028 6c69 6e65 2033 3529 0a0a s. (line 35)..\n+0001f5e0: 1f0a 4669 6c65 3a20 736b 6574 6368 2e69 ..File: sketch.i\n+0001f5f0: 6e66 6f2c 2020 4e6f 6465 3a20 496e 6465 nfo, Node: Inde\n+0001f600: 782c 2020 5072 6576 3a20 496e 6465 7820 x, Prev: Index \n+0001f610: 6f66 2073 796e 7461 782c 2020 5570 3a20 of syntax, Up: \n+0001f620: 546f 700a 0a49 6e64 6578 206f 6620 636f Top..Index of co\n+0001f630: 6e63 6570 7473 0a2a 2a2a 2a2a 2a2a 2a2a ncepts.*********\n+0001f640: 2a2a 2a2a 2a2a 2a2a 0a0a 0008 5b69 6e64 ********....[ind\n+0001f650: 6578 0008 5d0a 2a20 4d65 6e75 3a0a 0a2a ex..].* Menu:..*\n+0001f660: 2061 6666 696e 6520 6172 6974 686d 6574 affine arithmet\n+0001f670: 6963 3a20 2020 2020 2020 2020 2020 2020 ic: \n+0001f680: 2020 2020 2020 2020 4166 6669 6e65 2061 Affine a\n+0001f690: 7269 7468 6d65 7469 632e 2020 2028 6c69 rithmetic. (li\n+0001f6a0: 6e65 2020 2038 290a 2a20 6166 6669 6e65 ne 8).* affine\n+0001f6b0: 2061 7269 7468 6d65 7469 6320 3c31 3e3a arithmetic <1>:\n+0001f6c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f6d0: 2041 2074 6563 686e 6963 616c 2064 7261 A technical dra\n+0001f6e0: 7769 6e67 2e20 286c 696e 6520 2034 3029 wing. (line 40)\n+0001f6f0: 0a2a 2061 6c74 6572 6e61 7469 7665 732c .* alternatives,\n+0001f700: 2064 6566 696e 6974 696f 6e3a 2020 2020 definition: \n+0001f710: 2020 2020 2020 2020 2020 466f 726d 7320 Forms \n+0001f720: 6f66 2064 6566 696e 6974 696f 6e73 2e0a of definitions..\n+0001f730: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f740: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f750: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f760: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f770: 286c 696e 6520 2020 3629 0a2a 2061 7267 (line 6).* arg\n-0001f780: 756d 656e 742c 2073 7065 6369 616c 3a20 ument, special: \n+0001f760: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001f770: 696e 6520 2020 3629 0a2a 2061 7267 756d ine 6).* argum\n+0001f780: 656e 742c 2073 7065 6369 616c 3a20 2020 ent, special: \n 0001f790: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f7a0: 2020 2020 5370 6563 6961 6c20 6f62 6a65 Special obje\n-0001f7b0: 6374 732e 2020 2020 2028 6c69 6e65 2020 cts. (line \n-0001f7c0: 3235 290a 2a20 6172 6775 6d65 6e74 2c20 25).* argument, \n-0001f7d0: 7370 6563 6961 6c20 3c31 3e3a 2020 2020 special <1>: \n-0001f7e0: 2020 2020 2020 2020 2020 2020 2053 7065 Spe\n-0001f7f0: 6369 616c 732e 2020 2020 2020 2020 2020 cials. \n-0001f800: 2020 286c 696e 6520 2031 3029 0a2a 2061 (line 10).* a\n-0001f810: 7373 6f63 6961 7469 7669 7479 2c20 6f70 ssociativity, op\n-0001f820: 6572 6174 6f72 3a20 2020 2020 2020 2020 erator: \n-0001f830: 2020 2020 2020 5477 6f2d 6f70 6572 616e Two-operan\n-0001f840: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n-0001f850: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+0001f7a0: 2020 5370 6563 6961 6c20 6f62 6a65 6374 Special object\n+0001f7b0: 732e 2020 2020 2028 6c69 6e65 2020 3235 s. (line 25\n+0001f7c0: 290a 2a20 6172 6775 6d65 6e74 2c20 7370 ).* argument, sp\n+0001f7d0: 6563 6961 6c20 3c31 3e3a 2020 2020 2020 ecial <1>: \n+0001f7e0: 2020 2020 2020 2020 2020 2053 7065 6369 Speci\n+0001f7f0: 616c 732e 2020 2020 2020 2020 2020 2020 als. \n+0001f800: 286c 696e 6520 2031 3029 0a2a 2061 7373 (line 10).* ass\n+0001f810: 6f63 6961 7469 7669 7479 2c20 6f70 6572 ociativity, oper\n+0001f820: 6174 6f72 3a20 2020 2020 2020 2020 2020 ator: \n+0001f830: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n+0001f840: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+0001f850: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f860: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f870: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f880: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f890: 286c 696e 6520 2035 3829 0a2a 2061 7869 (line 58).* axi\n-0001f8a0: 732c 2072 6f74 6174 696f 6e3a 2020 2020 s, rotation: \n+0001f880: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001f890: 696e 6520 2035 3829 0a2a 2061 7869 732c ine 58).* axis,\n+0001f8a0: 2072 6f74 6174 696f 6e3a 2020 2020 2020 rotation: \n 0001f8b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f8c0: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n-0001f8d0: 666f 726d 732e 2020 2028 6c69 6e65 2020 forms. (line \n-0001f8e0: 3430 290a 2a20 6261 636b 2066 6163 653a 40).* back face:\n+0001f8c0: 2020 4f62 6a65 6374 2074 7261 6e73 666f Object transfo\n+0001f8d0: 726d 732e 2020 2028 6c69 6e65 2020 3430 rms. (line 40\n+0001f8e0: 290a 2a20 6261 636b 2066 6163 653a 2020 ).* back face: \n 0001f8f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f900: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n-0001f910: 7769 6e67 2061 2073 6f6c 6964 2e20 2020 wing a solid. \n-0001f920: 2020 286c 696e 6520 2033 3529 0a2a 2062 (line 35).* b\n-0001f930: 6173 656c 696e 6520 6672 6163 7469 6f6e aseline fraction\n-0001f940: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001f950: 2020 2020 2020 5069 6374 7572 6520 626f Picture bo\n-0001f960: 782e 2020 2020 2020 2020 2028 6c69 6e65 x. (line\n-0001f970: 2020 3130 290a 2a20 6269 6e61 7279 2066 10).* binary f\n-0001f980: 6f72 6d3a 2020 2020 2020 2020 2020 2020 orm: \n-0001f990: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-0001f9a0: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n-0001f9b0: 7279 2920 666f 726d 732e 0a20 2020 2020 ry) forms.. \n+0001f900: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+0001f910: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n+0001f920: 286c 696e 6520 2033 3529 0a2a 2062 6173 (line 35).* bas\n+0001f930: 656c 696e 6520 6672 6163 7469 6f6e 3a20 eline fraction: \n+0001f940: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001f950: 2020 2020 5069 6374 7572 6520 626f 782e Picture box.\n+0001f960: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+0001f970: 3130 290a 2a20 6269 6e61 7279 2066 6f72 10).* binary for\n+0001f980: 6d3a 2020 2020 2020 2020 2020 2020 2020 m: \n+0001f990: 2020 2020 2020 2020 2020 2020 2054 776f Two\n+0001f9a0: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n+0001f9b0: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n 0001f9c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f9d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001f9e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001f9f0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-0001fa00: 2036 290a 2a20 6269 6e61 7279 2073 7061 6).* binary spa\n-0001fa10: 6365 2070 6172 7469 7469 6f6e 3a20 2020 ce partition: \n-0001fa20: 2020 2020 2020 2020 2020 2020 2048 6964 Hid\n-0001fa30: 6465 6e20 7375 7266 6163 6520 7265 6d6f den surface remo\n-0001fa40: 7661 6c2e 0a20 2020 2020 2020 2020 2020 val.. \n+0001f9f0: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+0001fa00: 290a 2a20 6269 6e61 7279 2073 7061 6365 ).* binary space\n+0001fa10: 2070 6172 7469 7469 6f6e 3a20 2020 2020 partition: \n+0001fa20: 2020 2020 2020 2020 2020 2048 6964 6465 Hidde\n+0001fa30: 6e20 7375 7266 6163 6520 7265 6d6f 7661 n surface remova\n+0001fa40: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 0001fa50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001fa60: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001fa70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fa80: 2020 2028 6c69 6e65 2020 3233 290a 2a20 (line 23).* \n-0001fa90: 6269 6e61 7279 2073 7061 6365 2070 6172 binary space par\n-0001faa0: 7469 7469 6f6e 203c 313e 3a20 2020 2020 tition <1>: \n-0001fab0: 2020 2020 2020 2053 7461 7469 7374 6963 Statistic\n-0001fac0: 732e 2020 2020 2020 2020 2020 286c 696e s. (lin\n-0001fad0: 6520 2031 3329 0a2a 2062 696e 6172 7920 e 13).* binary \n-0001fae0: 7370 6163 6520 7061 7274 6974 696f 6e20 space partition \n-0001faf0: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n-0001fb00: 436f 6d6d 616e 6420 6c69 6e65 2e20 2020 Command line. \n-0001fb10: 2020 2020 2028 6c69 6e65 2020 3236 290a (line 26).\n-0001fb20: 2a20 626c 6f63 6b3a 2020 2020 2020 2020 * block: \n+0001fa80: 2028 6c69 6e65 2020 3233 290a 2a20 6269 (line 23).* bi\n+0001fa90: 6e61 7279 2073 7061 6365 2070 6172 7469 nary space parti\n+0001faa0: 7469 6f6e 203c 313e 3a20 2020 2020 2020 tion <1>: \n+0001fab0: 2020 2020 2053 7461 7469 7374 6963 732e Statistics.\n+0001fac0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+0001fad0: 2031 3329 0a2a 2062 696e 6172 7920 7370 13).* binary sp\n+0001fae0: 6163 6520 7061 7274 6974 696f 6e20 3c32 ace partition <2\n+0001faf0: 3e3a 2020 2020 2020 2020 2020 2020 436f >: Co\n+0001fb00: 6d6d 616e 6420 6c69 6e65 2e20 2020 2020 mmand line. \n+0001fb10: 2020 2028 6c69 6e65 2020 3236 290a 2a20 (line 26).* \n+0001fb20: 626c 6f63 6b3a 2020 2020 2020 2020 2020 block: \n 0001fb30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fb40: 2020 2020 2020 2020 204f 626a 6563 7420 Object \n-0001fb50: 7472 616e 7366 6f72 6d73 2e20 2020 286c transforms. (l\n-0001fb60: 696e 6520 2032 3429 0a2a 2062 6c6f 636b ine 24).* block\n-0001fb70: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+0001fb40: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n+0001fb50: 616e 7366 6f72 6d73 2e20 2020 286c 696e ansforms. (lin\n+0001fb60: 6520 2032 3429 0a2a 2062 6c6f 636b 203c e 24).* block <\n+0001fb70: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n 0001fb80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fb90: 2020 5377 6570 7420 626c 6f63 6b73 2e20 Swept blocks. \n-0001fba0: 2020 2020 2020 2028 6c69 6e65 2020 2037 (line 7\n-0001fbb0: 290a 2a20 626c 6f63 6b20 3c32 3e3a 2020 ).* block <2>: \n+0001fb90: 5377 6570 7420 626c 6f63 6b73 2e20 2020 Swept blocks. \n+0001fba0: 2020 2020 2028 6c69 6e65 2020 2037 290a (line 7).\n+0001fbb0: 2a20 626c 6f63 6b20 3c32 3e3a 2020 2020 * block <2>: \n 0001fbc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fbd0: 2020 2020 2020 2020 2020 2042 6c6f 636b Block\n-0001fbe0: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n-0001fbf0: 286c 696e 6520 2020 3629 0a2a 2062 6c6f (line 6).* blo\n-0001fc00: 636b 2073 7765 6570 3a20 2020 2020 2020 ck sweep: \n+0001fbd0: 2020 2020 2020 2020 2042 6c6f 636b 732e Blocks.\n+0001fbe0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+0001fbf0: 696e 6520 2020 3629 0a2a 2062 6c6f 636b ine 6).* block\n+0001fc00: 2073 7765 6570 3a20 2020 2020 2020 2020 sweep: \n 0001fc10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fc20: 2020 2020 5377 6570 7420 626c 6f63 6b73 Swept blocks\n-0001fc30: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n-0001fc40: 2036 290a 2a20 626f 6479 2070 6f6c 7967 6).* body polyg\n-0001fc50: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n-0001fc60: 2020 2020 2020 2020 2020 2020 2049 6e74 Int\n-0001fc70: 6572 6e61 6c20 6f70 7469 6f6e 732e 2020 ernal options. \n-0001fc80: 2020 286c 696e 6520 2031 3629 0a2a 2062 (line 16).* b\n-0001fc90: 6f64 7920 706f 6c79 676f 6e20 3c31 3e3a ody polygon <1>:\n+0001fc20: 2020 5377 6570 7420 626c 6f63 6b73 2e20 Swept blocks. \n+0001fc30: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+0001fc40: 290a 2a20 626f 6479 2070 6f6c 7967 6f6e ).* body polygon\n+0001fc50: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001fc60: 2020 2020 2020 2020 2020 2049 6e74 6572 Inter\n+0001fc70: 6e61 6c20 6f70 7469 6f6e 732e 2020 2020 nal options. \n+0001fc80: 286c 696e 6520 2031 3629 0a2a 2062 6f64 (line 16).* bod\n+0001fc90: 7920 706f 6c79 676f 6e20 3c31 3e3a 2020 y polygon <1>: \n 0001fca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fcb0: 2020 2020 2020 5377 6570 7420 6c69 6e65 Swept line\n-0001fcc0: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-0001fcd0: 2020 3130 290a 2a20 626f 6479 2070 6f6c 10).* body pol\n-0001fce0: 7967 6f6e 203c 323e 3a20 2020 2020 2020 ygon <2>: \n-0001fcf0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-0001fd00: 7765 7074 2070 6f6c 7967 6f6e 732e 2020 wept polygons. \n-0001fd10: 2020 2020 286c 696e 6520 2020 3929 0a2a (line 9).*\n-0001fd20: 2062 6f75 6e64 696e 6720 626f 783a 2020 bounding box: \n+0001fcb0: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n+0001fcc0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+0001fcd0: 3130 290a 2a20 626f 6479 2070 6f6c 7967 10).* body polyg\n+0001fce0: 6f6e 203c 323e 3a20 2020 2020 2020 2020 on <2>: \n+0001fcf0: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+0001fd00: 7074 2070 6f6c 7967 6f6e 732e 2020 2020 pt polygons. \n+0001fd10: 2020 286c 696e 6520 2020 3929 0a2a 2062 (line 9).* b\n+0001fd20: 6f75 6e64 696e 6720 626f 783a 2020 2020 ounding box: \n 0001fd30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fd40: 2020 2020 2020 2020 5069 6374 7572 6520 Picture \n-0001fd50: 626f 782e 2020 2020 2020 2020 2028 6c69 box. (li\n-0001fd60: 6e65 2020 3135 290a 2a20 4253 502c 2062 ne 15).* BSP, b\n-0001fd70: 696e 6172 7920 7370 6163 6520 7061 7274 inary space part\n-0001fd80: 6974 696f 6e3a 2020 2020 2020 2020 2020 ition: \n-0001fd90: 2048 6964 6465 6e20 7375 7266 6163 6520 Hidden surface \n-0001fda0: 7265 6d6f 7661 6c2e 0a20 2020 2020 2020 removal.. \n+0001fd40: 2020 2020 2020 5069 6374 7572 6520 626f Picture bo\n+0001fd50: 782e 2020 2020 2020 2020 2028 6c69 6e65 x. (line\n+0001fd60: 2020 3135 290a 2a20 4253 502c 2062 696e 15).* BSP, bin\n+0001fd70: 6172 7920 7370 6163 6520 7061 7274 6974 ary space partit\n+0001fd80: 696f 6e3a 2020 2020 2020 2020 2020 2048 ion: H\n+0001fd90: 6964 6465 6e20 7375 7266 6163 6520 7265 idden surface re\n+0001fda0: 6d6f 7661 6c2e 0a20 2020 2020 2020 2020 moval.. \n 0001fdb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001fdc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 0001fdd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fde0: 2020 2020 2020 2028 6c69 6e65 2020 3233 (line 23\n-0001fdf0: 290a 2a20 4253 502c 2062 696e 6172 7920 ).* BSP, binary \n-0001fe00: 7370 6163 6520 7061 7274 6974 696f 6e20 space partition \n-0001fe10: 3c31 3e3a 2020 2020 2020 2043 6f6d 6d61 <1>: Comma\n-0001fe20: 6e64 206c 696e 652e 2020 2020 2020 2020 nd line. \n-0001fe30: 286c 696e 6520 2032 3629 0a2a 2063 616d (line 26).* cam\n-0001fe40: 6572 613a 2020 2020 2020 2020 2020 2020 era: \n+0001fde0: 2020 2020 2028 6c69 6e65 2020 3233 290a (line 23).\n+0001fdf0: 2a20 4253 502c 2062 696e 6172 7920 7370 * BSP, binary sp\n+0001fe00: 6163 6520 7061 7274 6974 696f 6e20 3c31 ace partition <1\n+0001fe10: 3e3a 2020 2020 2020 2043 6f6d 6d61 6e64 >: Command\n+0001fe20: 206c 696e 652e 2020 2020 2020 2020 286c line. (l\n+0001fe30: 696e 6520 2032 3629 0a2a 2063 616d 6572 ine 26).* camer\n+0001fe40: 613a 2020 2020 2020 2020 2020 2020 2020 a: \n 0001fe50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001fe60: 2020 2020 4361 6d65 7261 2e20 2020 2020 Camera. \n-0001fe70: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-0001fe80: 2036 290a 2a20 6365 6e74 6572 206f 6620 6).* center of \n-0001fe90: 726f 7461 7469 6f6e 3a20 2020 2020 2020 rotation: \n-0001fea0: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n-0001feb0: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n-0001fec0: 2020 286c 696e 6520 2020 3829 0a2a 2063 (line 8).* c\n-0001fed0: 656e 7465 7220 6f66 2072 6f74 6174 696f enter of rotatio\n-0001fee0: 6e20 3c31 3e3a 2020 2020 2020 2020 2020 n <1>: \n-0001fef0: 2020 2020 2020 4e65 7374 6564 2073 7765 Nested swe\n-0001ff00: 6570 732e 2020 2020 2020 2028 6c69 6e65 eps. (line\n-0001ff10: 2020 2036 290a 2a20 6365 6e74 726f 6964 6).* centroid\n-0001ff20: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-0001ff30: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-0001ff40: 2074 6563 686e 6963 616c 2064 7261 7769 technical drawi\n-0001ff50: 6e67 2e20 286c 696e 6520 2036 3429 0a2a ng. (line 64).*\n-0001ff60: 2063 656e 7472 6f69 6420 3c31 3e3a 2020 centroid <1>: \n+0001fe60: 2020 4361 6d65 7261 2e20 2020 2020 2020 Camera. \n+0001fe70: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+0001fe80: 290a 2a20 6365 6e74 6572 206f 6620 726f ).* center of ro\n+0001fe90: 7461 7469 6f6e 3a20 2020 2020 2020 2020 tation: \n+0001fea0: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n+0001feb0: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n+0001fec0: 286c 696e 6520 2020 3829 0a2a 2063 656e (line 8).* cen\n+0001fed0: 7465 7220 6f66 2072 6f74 6174 696f 6e20 ter of rotation \n+0001fee0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n+0001fef0: 2020 2020 4e65 7374 6564 2073 7765 6570 Nested sweep\n+0001ff00: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. (line \n+0001ff10: 2036 290a 2a20 6365 6e74 726f 6964 3a20 6).* centroid: \n+0001ff20: 2020 2020 2020 2020 2020 2020 2020 2020 \n+0001ff30: 2020 2020 2020 2020 2020 2020 2041 2074 A t\n+0001ff40: 6563 686e 6963 616c 2064 7261 7769 6e67 echnical drawing\n+0001ff50: 2e20 286c 696e 6520 2036 3429 0a2a 2063 . (line 64).* c\n+0001ff60: 656e 7472 6f69 6420 3c31 3e3a 2020 2020 entroid <1>: \n 0001ff70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ff80: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n-0001ff90: 6361 6c20 6472 6177 696e 672e 2028 6c69 cal drawing. (li\n-0001ffa0: 6e65 2031 3032 290a 2a20 636c 6970 7069 ne 102).* clippi\n-0001ffb0: 6e67 3a20 2020 2020 2020 2020 2020 2020 ng: \n-0001ffc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-0001ffd0: 2050 6963 7475 7265 2062 6f78 2e20 2020 Picture box. \n-0001ffe0: 2020 2020 2020 286c 696e 6520 2031 3729 (line 17)\n-0001fff0: 0a2a 2063 6c69 7070 696e 6720 3c31 3e3a .* clipping <1>:\n+0001ff80: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n+0001ff90: 6c20 6472 6177 696e 672e 2028 6c69 6e65 l drawing. (line\n+0001ffa0: 2031 3032 290a 2a20 636c 6970 7069 6e67 102).* clipping\n+0001ffb0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+0001ffc0: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+0001ffd0: 6963 7475 7265 2062 6f78 2e20 2020 2020 icture box. \n+0001ffe0: 2020 2020 286c 696e 6520 2031 3729 0a2a (line 17).*\n+0001fff0: 2063 6c69 7070 696e 6720 3c31 3e3a 2020 clipping <1>: \n 00020000: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020010: 2020 2020 2020 2020 2020 436c 6970 7069 Clippi\n-00020020: 6e67 2e20 2020 2020 2020 2020 2020 2028 ng. (\n-00020030: 6c69 6e65 2020 2036 290a 2a20 636c 6f73 line 6).* clos\n-00020040: 7572 6520 7461 672c 203c 3e3a 2020 2020 ure tag, <>: \n+00020010: 2020 2020 2020 2020 436c 6970 7069 6e67 Clipping\n+00020020: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n+00020030: 6e65 2020 2036 290a 2a20 636c 6f73 7572 ne 6).* closur\n+00020040: 6520 7461 672c 203c 3e3a 2020 2020 2020 e tag, <>: \n 00020050: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020060: 2020 2050 6f69 6e74 2073 7765 6570 732e Point sweeps.\n-00020070: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n-00020080: 3829 0a2a 2063 6c6f 7375 7265 2074 6167 8).* closure tag\n-00020090: 2c20 3c3e 203c 313e 3a20 2020 2020 2020 , <> <1>: \n-000200a0: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-000200b0: 6c69 6e65 2073 7765 6570 7320 7769 7468 line sweeps with\n-000200c0: 2063 6c6f 7375 7265 2e0a 2020 2020 2020 closure.. \n+00020060: 2050 6f69 6e74 2073 7765 6570 732e 2020 Point sweeps. \n+00020070: 2020 2020 2020 286c 696e 6520 2031 3829 (line 18)\n+00020080: 0a2a 2063 6c6f 7375 7265 2074 6167 2c20 .* closure tag, \n+00020090: 3c3e 203c 313e 3a20 2020 2020 2020 2020 <> <1>: \n+000200a0: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n+000200b0: 6e65 2073 7765 6570 7320 7769 7468 2063 ne sweeps with c\n+000200c0: 6c6f 7375 7265 2e0a 2020 2020 2020 2020 losure.. \n 000200d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000200e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000200f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020100: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n-00020110: 3629 0a2a 2063 6c6f 7375 7265 2074 6167 6).* closure tag\n-00020120: 2c20 3c3e 203c 323e 3a20 2020 2020 2020 , <> <2>: \n-00020130: 2020 2020 2020 2020 2020 2020 5377 6565 Swee\n-00020140: 7073 2e20 2020 2020 2020 2020 2020 2020 ps. \n-00020150: 2028 6c69 6e65 2020 3139 290a 2a20 636c (line 19).* cl\n-00020160: 6f73 7572 6520 7461 672c 203c 3e20 3c33 osure tag, <> <3\n-00020170: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00020180: 2020 2020 2053 7765 7074 2070 6f69 6e74 Swept point\n-00020190: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n-000201a0: 2020 3629 0a2a 2063 6c6f 7375 7265 2074 6).* closure t\n-000201b0: 6167 2c20 3c3e 203c 343e 3a20 2020 2020 ag, <> <4>: \n-000201c0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-000201d0: 6570 7420 706f 696e 7473 2e20 2020 2020 ept points. \n-000201e0: 2020 2028 6c69 6e65 2020 3133 290a 2a20 (line 13).* \n-000201f0: 636c 6f73 7572 6520 7461 672c 203c 3e20 closure tag, <> \n-00020200: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n-00020210: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n-00020220: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n-00020230: 6520 2020 3629 0a2a 2063 6c6f 7375 7265 e 6).* closure\n-00020240: 2074 6167 2c20 3c3e 203c 363e 3a20 2020 tag, <> <6>: \n-00020250: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020260: 5377 6570 7420 6c69 6e65 732e 2020 2020 Swept lines. \n-00020270: 2020 2020 2028 6c69 6e65 2020 3238 290a (line 28).\n-00020280: 2a20 636c 6f73 7572 6520 7461 672c 203c * closure tag, <\n-00020290: 3e20 3c37 3e3a 2020 2020 2020 2020 2020 > <7>: \n-000202a0: 2020 2020 2020 2020 2053 7765 6570 2066 Sweep f\n-000202b0: 6163 6520 7370 6c69 7474 696e 672e 0a20 ace splitting.. \n+00020100: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n+00020110: 0a2a 2063 6c6f 7375 7265 2074 6167 2c20 .* closure tag, \n+00020120: 3c3e 203c 323e 3a20 2020 2020 2020 2020 <> <2>: \n+00020130: 2020 2020 2020 2020 2020 5377 6565 7073 Sweeps\n+00020140: 2e20 2020 2020 2020 2020 2020 2020 2028 . (\n+00020150: 6c69 6e65 2020 3139 290a 2a20 636c 6f73 line 19).* clos\n+00020160: 7572 6520 7461 672c 203c 3e20 3c33 3e3a ure tag, <> <3>:\n+00020170: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00020180: 2020 2053 7765 7074 2070 6f69 6e74 732e Swept points.\n+00020190: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+000201a0: 3629 0a2a 2063 6c6f 7375 7265 2074 6167 6).* closure tag\n+000201b0: 2c20 3c3e 203c 343e 3a20 2020 2020 2020 , <> <4>: \n+000201c0: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+000201d0: 7420 706f 696e 7473 2e20 2020 2020 2020 t points. \n+000201e0: 2028 6c69 6e65 2020 3133 290a 2a20 636c (line 13).* cl\n+000201f0: 6f73 7572 6520 7461 672c 203c 3e20 3c35 osure tag, <> <5\n+00020200: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00020210: 2020 2020 2053 7765 7074 206c 696e 6573 Swept lines\n+00020220: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+00020230: 2020 3629 0a2a 2063 6c6f 7375 7265 2074 6).* closure t\n+00020240: 6167 2c20 3c3e 203c 363e 3a20 2020 2020 ag, <> <6>: \n+00020250: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+00020260: 6570 7420 6c69 6e65 732e 2020 2020 2020 ept lines. \n+00020270: 2020 2028 6c69 6e65 2020 3238 290a 2a20 (line 28).* \n+00020280: 636c 6f73 7572 6520 7461 672c 203c 3e20 closure tag, <> \n+00020290: 3c37 3e3a 2020 2020 2020 2020 2020 2020 <7>: \n+000202a0: 2020 2020 2020 2053 7765 6570 2066 6163 Sweep fac\n+000202b0: 6520 7370 6c69 7474 696e 672e 0a20 2020 e splitting.. \n 000202c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000202d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000202e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000202f0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n-00020300: 6e65 2020 3131 290a 2a20 636f 6d6d 616e ne 11).* comman\n-00020310: 6420 6c69 6e65 206f 7074 696f 6e3a 2020 d line option: \n-00020320: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020330: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n-00020340: 2020 2020 2020 286c 696e 6520 2033 3029 (line 30)\n-00020350: 0a2a 2063 6f6d 6d61 6e64 206c 696e 6520 .* command line \n-00020360: 6f70 7469 6f6e 733a 2020 2020 2020 2020 options: \n-00020370: 2020 2020 2020 2020 2020 436f 6d6d 616e Comman\n-00020380: 6420 6c69 6e65 2e20 2020 2020 2020 2028 d line. (\n-00020390: 6c69 6e65 2020 3134 290a 2a20 636f 6d6d line 14).* comm\n-000203a0: 616e 6420 6c69 6e65 2c20 736b 6574 6368 and line, sketch\n-000203b0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000203c0: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20 Hello world. \n-000203d0: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n-000203e0: 3929 0a2a 2063 6f6d 6d61 6e64 206c 696e 9).* command lin\n-000203f0: 652c 2073 6b65 7463 6820 3c31 3e3a 2020 e, sketch <1>: \n-00020400: 2020 2020 2020 2020 2020 2020 436f 6d6d Comm\n-00020410: 616e 6420 6c69 6e65 2e20 2020 2020 2020 and line. \n-00020420: 2028 6c69 6e65 2020 2036 290a 2a20 636f (line 6).* co\n-00020430: 6d6d 656e 7473 3a20 2020 2020 2020 2020 mments: \n+000202f0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+00020300: 2020 3131 290a 2a20 636f 6d6d 616e 6420 11).* command \n+00020310: 6c69 6e65 206f 7074 696f 6e3a 2020 2020 line option: \n+00020320: 2020 2020 2020 2020 2020 2020 2020 2048 H\n+00020330: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020 ello world. \n+00020340: 2020 2020 286c 696e 6520 2033 3029 0a2a (line 30).*\n+00020350: 2063 6f6d 6d61 6e64 206c 696e 6520 6f70 command line op\n+00020360: 7469 6f6e 733a 2020 2020 2020 2020 2020 tions: \n+00020370: 2020 2020 2020 2020 436f 6d6d 616e 6420 Command \n+00020380: 6c69 6e65 2e20 2020 2020 2020 2028 6c69 line. (li\n+00020390: 6e65 2020 3134 290a 2a20 636f 6d6d 616e ne 14).* comman\n+000203a0: 6420 6c69 6e65 2c20 736b 6574 6368 3a20 d line, sketch: \n+000203b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000203c0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n+000203d0: 2020 2020 2020 286c 696e 6520 2020 3929 (line 9)\n+000203e0: 0a2a 2063 6f6d 6d61 6e64 206c 696e 652c .* command line,\n+000203f0: 2073 6b65 7463 6820 3c31 3e3a 2020 2020 sketch <1>: \n+00020400: 2020 2020 2020 2020 2020 436f 6d6d 616e Comman\n+00020410: 6420 6c69 6e65 2e20 2020 2020 2020 2028 d line. (\n+00020420: 6c69 6e65 2020 2036 290a 2a20 636f 6d6d line 6).* comm\n+00020430: 656e 7473 3a20 2020 2020 2020 2020 2020 ents: \n 00020440: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020450: 2020 2020 2044 7261 7769 6e67 2061 2073 Drawing a s\n-00020460: 6f6c 6964 2e20 2020 2020 286c 696e 6520 olid. (line \n-00020470: 2032 3829 0a2a 2063 6f6d 6d65 6e74 7320 28).* comments \n-00020480: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00020490: 2020 2020 2020 2020 2020 2020 2020 4c61 La\n-000204a0: 6e67 7561 6765 2062 6173 6963 732e 2020 nguage basics. \n-000204b0: 2020 2028 6c69 6e65 2020 3138 290a 2a20 (line 18).* \n-000204c0: 636f 6e73 7472 7563 746f 723a 2020 2020 constructor: \n+00020450: 2020 2044 7261 7769 6e67 2061 2073 6f6c Drawing a sol\n+00020460: 6964 2e20 2020 2020 286c 696e 6520 2032 id. (line 2\n+00020470: 3829 0a2a 2063 6f6d 6d65 6e74 7320 3c31 8).* comments <1\n+00020480: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00020490: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n+000204a0: 7561 6765 2062 6173 6963 732e 2020 2020 uage basics. \n+000204b0: 2028 6c69 6e65 2020 3138 290a 2a20 636f (line 18).* co\n+000204c0: 6e73 7472 7563 746f 723a 2020 2020 2020 nstructor: \n 000204d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000204e0: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-000204f0: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-00020500: 6520 2020 3629 0a2a 2063 6f6f 7264 696e e 6).* coordin\n-00020510: 6174 6520 7379 7374 656d 2c20 7269 6768 ate system, righ\n-00020520: 742d 6861 6e64 6564 3a20 2020 2020 2020 t-handed: \n-00020530: 496e 7472 6f64 7563 7469 6f6e 2062 7920 Introduction by \n-00020540: 6578 616d 706c 652e 0a20 2020 2020 2020 example.. \n+000204e0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+000204f0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+00020500: 2020 3629 0a2a 2063 6f6f 7264 696e 6174 6).* coordinat\n+00020510: 6520 7379 7374 656d 2c20 7269 6768 742d e system, right-\n+00020520: 6861 6e64 6564 3a20 2020 2020 2020 496e handed: In\n+00020530: 7472 6f64 7563 7469 6f6e 2062 7920 6578 troduction by ex\n+00020540: 616d 706c 652e 0a20 2020 2020 2020 2020 ample.. \n 00020550: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020560: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020570: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020580: 2020 2020 2020 2028 6c69 6e65 2020 3131 (line 11\n-00020590: 290a 2a20 636f 756e 7465 722d 636c 6f63 ).* counter-cloc\n-000205a0: 6b77 6973 6520 706f 6c79 676f 6e20 7665 kwise polygon ve\n-000205b0: 7274 6578 206f 7264 6572 3a20 4865 6c6c rtex order: Hell\n-000205c0: 6f20 776f 726c 642e 2020 2020 2020 2020 o world. \n-000205d0: 286c 696e 6520 2033 3929 0a2a 2063 756c (line 39).* cul\n-000205e0: 6c69 6e67 3a20 2020 2020 2020 2020 2020 ling: \n+00020580: 2020 2020 2028 6c69 6e65 2020 3131 290a (line 11).\n+00020590: 2a20 636f 756e 7465 722d 636c 6f63 6b77 * counter-clockw\n+000205a0: 6973 6520 706f 6c79 676f 6e20 7665 7274 ise polygon vert\n+000205b0: 6578 206f 7264 6572 3a20 4865 6c6c 6f20 ex order: Hello \n+000205c0: 776f 726c 642e 2020 2020 2020 2020 286c world. 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(line\n-000206b0: 2020 3431 290a 2a20 6375 6c6c 696e 6720 41).* culling \n-000206c0: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n-000206d0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-000206e0: 7765 7074 206c 696e 6573 2e20 2020 2020 wept lines. \n-000206f0: 2020 2020 286c 696e 6520 2031 3629 0a2a (line 16).*\n-00020700: 2064 6563 6c61 7261 7469 7665 206c 616e declarative lan\n-00020710: 6775 6167 653a 2020 2020 2020 2020 2020 guage: \n-00020720: 2020 2020 2020 2020 4c61 6e67 7561 6765 Language\n-00020730: 2062 6173 6963 732e 2020 2020 2028 6c69 basics. (li\n-00020740: 6e65 2020 2038 290a 2a20 6465 6669 6e69 ne 8).* defini\n-00020750: 7469 6f6e 3a20 2020 2020 2020 2020 2020 tion: \n-00020760: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020770: 2044 7261 7769 6e67 2061 2073 6f6c 6964 Drawing a solid\n-00020780: 2e20 2020 2020 286c 696e 6520 2032 3229 . (line 22)\n-00020790: 0a2a 2064 6566 696e 6974 696f 6e20 3c31 .* definition <1\n-000207a0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-000207b0: 2020 2020 2020 2020 2020 4465 6669 6e69 Defini\n-000207c0: 7469 6f6e 732e 2020 2020 2020 2020 2028 tions. (\n-000207d0: 6c69 6e65 2020 2036 290a 2a20 6465 6669 line 6).* defi\n-000207e0: 6e69 7469 6f6e 2077 6974 6820 616c 7465 nition with alte\n-000207f0: 726e 6174 6976 6573 3a20 2020 2020 2020 rnatives: \n-00020800: 2020 2046 6f72 6d73 206f 6620 6465 6669 Forms of defi\n-00020810: 6e69 7469 6f6e 732e 0a20 2020 2020 2020 nitions.. \n+00020690: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n+000206a0: 6c69 642e 2020 2020 2028 6c69 6e65 2020 lid. (line \n+000206b0: 3431 290a 2a20 6375 6c6c 696e 6720 3c33 41).* culling <3\n+000206c0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+000206d0: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+000206e0: 7074 206c 696e 6573 2e20 2020 2020 2020 pt lines. \n+000206f0: 2020 286c 696e 6520 2031 3629 0a2a 2064 (line 16).* d\n+00020700: 6563 6c61 7261 7469 7665 206c 616e 6775 eclarative langu\n+00020710: 6167 653a 2020 2020 2020 2020 2020 2020 age: \n+00020720: 2020 2020 2020 4c61 6e67 7561 6765 2062 Language b\n+00020730: 6173 6963 732e 2020 2020 2028 6c69 6e65 asics. (line\n+00020740: 2020 2038 290a 2a20 6465 6669 6e69 7469 8).* definiti\n+00020750: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n+00020760: 2020 2020 2020 2020 2020 2020 2020 2044 D\n+00020770: 7261 7769 6e67 2061 2073 6f6c 6964 2e20 rawing a solid. \n+00020780: 2020 2020 286c 696e 6520 2032 3229 0a2a (line 22).*\n+00020790: 2064 6566 696e 6974 696f 6e20 3c31 3e3a definition <1>:\n+000207a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000207b0: 2020 2020 2020 2020 4465 6669 6e69 7469 Definiti\n+000207c0: 6f6e 732e 2020 2020 2020 2020 2028 6c69 ons. (li\n+000207d0: 6e65 2020 2036 290a 2a20 6465 6669 6e69 ne 6).* defini\n+000207e0: 7469 6f6e 2077 6974 6820 616c 7465 726e tion with altern\n+000207f0: 6174 6976 6573 3a20 2020 2020 2020 2020 atives: \n+00020800: 2046 6f72 6d73 206f 6620 6465 6669 6e69 Forms of defini\n+00020810: 7469 6f6e 732e 0a20 2020 2020 2020 2020 tions.. \n 00020820: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020830: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020840: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020850: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n-00020860: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20 ).* definition, \n-00020870: 6472 6177 6162 6c65 3a20 2020 2020 2020 drawable: \n-00020880: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n-00020890: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n-000208a0: 286c 696e 6520 2032 3729 0a2a 2064 6566 (line 27).* def\n-000208b0: 696e 6974 696f 6e2c 206f 7074 696f 6e73 inition, options\n-000208c0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000208d0: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n-000208e0: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n-000208f0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00020850: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+00020860: 2a20 6465 6669 6e69 7469 6f6e 2c20 6472 * definition, dr\n+00020870: 6177 6162 6c65 3a20 2020 2020 2020 2020 awable: \n+00020880: 2020 2020 2020 2020 204f 626a 6563 7420 Object \n+00020890: 7472 616e 7366 6f72 6d73 2e20 2020 286c transforms. (l\n+000208a0: 696e 6520 2032 3729 0a2a 2064 6566 696e ine 27).* defin\n+000208b0: 6974 696f 6e2c 206f 7074 696f 6e73 3a20 ition, options: \n+000208c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000208d0: 2020 506f 6c79 6c69 6e65 2073 7765 6570 Polyline sweep\n+000208e0: 7320 7769 7468 2063 6c6f 7375 7265 2e0a s with closure..\n+000208f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020900: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020910: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020920: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020930: 286c 696e 6520 2032 3329 0a2a 2064 6566 (line 23).* def\n-00020940: 696e 6974 696f 6e2c 2070 6f69 6e74 3a20 inition, point: \n+00020920: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00020930: 696e 6520 2032 3329 0a2a 2064 6566 696e ine 23).* defin\n+00020940: 6974 696f 6e2c 2070 6f69 6e74 3a20 2020 ition, point: \n 00020950: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020960: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n-00020970: 6c69 642e 2020 2020 2028 6c69 6e65 2020 lid. (line \n-00020980: 3233 290a 2a20 6465 6669 6e69 7469 6f6e 23).* definition\n-00020990: 2c20 7363 616c 6172 3a20 2020 2020 2020 , scalar: \n-000209a0: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-000209b0: 7074 206f 626a 6563 7473 2e20 2020 2020 pt objects. \n-000209c0: 2020 286c 696e 6520 2031 3329 0a2a 2064 (line 13).* d\n-000209d0: 6566 696e 6974 696f 6e2c 2073 696d 706c efinition, simpl\n-000209e0: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-000209f0: 2020 2020 2020 466f 726d 7320 6f66 2064 Forms of d\n-00020a00: 6566 696e 6974 696f 6e73 2e0a 2020 2020 efinitions.. \n+00020960: 2020 4472 6177 696e 6720 6120 736f 6c69 Drawing a soli\n+00020970: 642e 2020 2020 2028 6c69 6e65 2020 3233 d. (line 23\n+00020980: 290a 2a20 6465 6669 6e69 7469 6f6e 2c20 ).* definition, \n+00020990: 7363 616c 6172 3a20 2020 2020 2020 2020 scalar: \n+000209a0: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+000209b0: 206f 626a 6563 7473 2e20 2020 2020 2020 objects. \n+000209c0: 286c 696e 6520 2031 3329 0a2a 2064 6566 (line 13).* def\n+000209d0: 696e 6974 696f 6e2c 2073 696d 706c 653a inition, simple:\n+000209e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000209f0: 2020 2020 466f 726d 7320 6f66 2064 6566 Forms of def\n+00020a00: 696e 6974 696f 6e73 2e0a 2020 2020 2020 initions.. \n 00020a10: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020a20: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020a30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020a40: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00020a50: 2020 3629 0a2a 2064 6566 696e 6974 696f 6).* definitio\n-00020a60: 6e2c 2074 6167 3a20 2020 2020 2020 2020 n, tag: \n-00020a70: 2020 2020 2020 2020 2020 2020 2020 4465 De\n-00020a80: 6669 6e69 7469 6f6e 732e 2020 2020 2020 finitions. \n-00020a90: 2020 2028 6c69 6e65 2020 3138 290a 2a20 (line 18).* \n-00020aa0: 6465 6669 6e69 7469 6f6e 2c20 7461 6720 definition, tag \n-00020ab0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00020ac0: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n-00020ad0: 6465 6669 6e69 7469 6f6e 732e 0a20 2020 definitions.. \n+00020a40: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+00020a50: 3629 0a2a 2064 6566 696e 6974 696f 6e2c 6).* definition,\n+00020a60: 2074 6167 3a20 2020 2020 2020 2020 2020 tag: \n+00020a70: 2020 2020 2020 2020 2020 2020 4465 6669 Defi\n+00020a80: 6e69 7469 6f6e 732e 2020 2020 2020 2020 nitions. \n+00020a90: 2028 6c69 6e65 2020 3138 290a 2a20 6465 (line 18).* de\n+00020aa0: 6669 6e69 7469 6f6e 2c20 7461 6720 3c31 finition, tag <1\n+00020ab0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00020ac0: 2020 2020 2046 6f72 6d73 206f 6620 6465 Forms of de\n+00020ad0: 6669 6e69 7469 6f6e 732e 0a20 2020 2020 finitions.. \n 00020ae0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020af0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020b00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020b10: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00020b20: 2020 2037 290a 2a20 6465 6669 6e69 7469 7).* definiti\n-00020b30: 6f6e 2c20 7461 6720 3c32 3e3a 2020 2020 on, tag <2>: \n-00020b40: 2020 2020 2020 2020 2020 2020 2020 2043 C\n-00020b50: 6f6d 6d61 6e64 206c 696e 652e 2020 2020 ommand line. \n-00020b60: 2020 2020 286c 696e 6520 2035 3329 0a2a (line 53).*\n-00020b70: 2064 6566 696e 6974 696f 6e2c 2074 7261 definition, tra\n-00020b80: 6e73 666f 726d 3a20 2020 2020 2020 2020 nsform: \n-00020b90: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n-00020ba0: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n-00020bb0: 6e65 2020 3335 290a 2a20 6465 6669 6e69 ne 35).* defini\n-00020bc0: 7469 6f6e 2c20 7665 6374 6f72 3a20 2020 tion, vector: \n-00020bd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020be0: 2050 6f6c 796c 696e 6520 7377 6565 7073 Polyline sweeps\n-00020bf0: 2e20 2020 2020 286c 696e 6520 2031 3929 . (line 19)\n-00020c00: 0a2a 2064 6570 7468 2073 6f72 743a 2020 .* depth sort: \n+00020b10: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00020b20: 2037 290a 2a20 6465 6669 6e69 7469 6f6e 7).* definition\n+00020b30: 2c20 7461 6720 3c32 3e3a 2020 2020 2020 , tag <2>: \n+00020b40: 2020 2020 2020 2020 2020 2020 2043 6f6d Com\n+00020b50: 6d61 6e64 206c 696e 652e 2020 2020 2020 mand line. \n+00020b60: 2020 286c 696e 6520 2035 3329 0a2a 2064 (line 53).* d\n+00020b70: 6566 696e 6974 696f 6e2c 2074 7261 6e73 efinition, trans\n+00020b80: 666f 726d 3a20 2020 2020 2020 2020 2020 form: \n+00020b90: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n+00020ba0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+00020bb0: 2020 3335 290a 2a20 6465 6669 6e69 7469 35).* definiti\n+00020bc0: 6f6e 2c20 7665 6374 6f72 3a20 2020 2020 on, vector: \n+00020bd0: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+00020be0: 6f6c 796c 696e 6520 7377 6565 7073 2e20 olyline sweeps. \n+00020bf0: 2020 2020 286c 696e 6520 2031 3929 0a2a (line 19).*\n+00020c00: 2064 6570 7468 2073 6f72 743a 2020 2020 depth sort: \n 00020c10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020c20: 2020 2020 2020 2020 2020 496e 7465 726e Intern\n-00020c30: 616c 206f 7074 696f 6e73 2e20 2020 2028 al options. (\n-00020c40: 6c69 6e65 2020 3133 290a 2a20 6465 7074 line 13).* dept\n-00020c50: 6820 736f 7274 203c 313e 3a20 2020 2020 h sort <1>: \n+00020c20: 2020 2020 2020 2020 496e 7465 726e 616c Internal\n+00020c30: 206f 7074 696f 6e73 2e20 2020 2028 6c69 options. (li\n+00020c40: 6e65 2020 3133 290a 2a20 6465 7074 6820 ne 13).* depth \n+00020c50: 736f 7274 203c 313e 3a20 2020 2020 2020 sort <1>: \n 00020c60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020c70: 2020 2048 6964 6465 6e20 7375 7266 6163 Hidden surfac\n-00020c80: 6520 7265 6d6f 7661 6c2e 0a20 2020 2020 e removal.. \n+00020c70: 2048 6964 6465 6e20 7375 7266 6163 6520 Hidden surface \n+00020c80: 7265 6d6f 7661 6c2e 0a20 2020 2020 2020 removal.. \n 00020c90: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020ca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00020cb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020cc0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00020cd0: 2036 290a 2a20 6465 7074 6820 736f 7274 6).* depth sort\n-00020ce0: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n-00020cf0: 2020 2020 2020 2020 2020 2020 2042 7567 Bug\n-00020d00: 7320 616e 6420 616e 6f6d 616c 6965 732e s and anomalies.\n-00020d10: 2020 286c 696e 6520 2020 3829 0a2a 2064 (line 8).* d\n-00020d20: 6972 6563 7420 7472 616e 7366 6f72 6d3a irect transform:\n+00020cc0: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+00020cd0: 290a 2a20 6465 7074 6820 736f 7274 203c ).* depth sort <\n+00020ce0: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n+00020cf0: 2020 2020 2020 2020 2020 2042 7567 7320 Bugs \n+00020d00: 616e 6420 616e 6f6d 616c 6965 732e 2020 and anomalies. \n+00020d10: 286c 696e 6520 2020 3829 0a2a 2064 6972 (line 8).* dir\n+00020d20: 6563 7420 7472 616e 7366 6f72 6d3a 2020 ect transform: \n 00020d30: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020d40: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n-00020d50: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65 literals. (line\n-00020d60: 2020 3437 290a 2a20 6469 7265 6374 2074 47).* direct t\n-00020d70: 7261 6e73 666f 726d 203c 313e 3a20 2020 ransform <1>: \n-00020d80: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-00020d90: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n-00020da0: 732e 2020 286c 696e 6520 2035 3329 0a2a s. (line 53).*\n-00020db0: 2064 6f63 756d 656e 7420 7465 6d70 6c61 document templa\n-00020dc0: 7465 3a20 2020 2020 2020 2020 2020 2020 te: \n-00020dd0: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n-00020de0: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n-00020df0: 6e65 2020 3332 290a 2a20 646f 6375 6d65 ne 32).* docume\n-00020e00: 6e74 2074 656d 706c 6174 6520 3c31 3e3a nt template <1>:\n-00020e10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020e20: 2043 6f6d 6d61 6e64 206c 696e 652e 2020 Command line. \n-00020e30: 2020 2020 2020 286c 696e 6520 2033 3629 (line 36)\n-00020e40: 0a2a 2064 7261 7761 626c 653a 2020 2020 .* drawable: \n+00020d40: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n+00020d50: 7465 7261 6c73 2e20 2028 6c69 6e65 2020 terals. (line \n+00020d60: 3437 290a 2a20 6469 7265 6374 2074 7261 47).* direct tra\n+00020d70: 6e73 666f 726d 203c 313e 3a20 2020 2020 nsform <1>: \n+00020d80: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n+00020d90: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n+00020da0: 2020 286c 696e 6520 2035 3329 0a2a 2064 (line 53).* d\n+00020db0: 6f63 756d 656e 7420 7465 6d70 6c61 7465 ocument template\n+00020dc0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00020dd0: 2020 2020 2020 4865 6c6c 6f20 776f 726c Hello worl\n+00020de0: 642e 2020 2020 2020 2020 2028 6c69 6e65 d. (line\n+00020df0: 2020 3332 290a 2a20 646f 6375 6d65 6e74 32).* document\n+00020e00: 2074 656d 706c 6174 6520 3c31 3e3a 2020 template <1>: \n+00020e10: 2020 2020 2020 2020 2020 2020 2020 2043 C\n+00020e20: 6f6d 6d61 6e64 206c 696e 652e 2020 2020 ommand line. \n+00020e30: 2020 2020 286c 696e 6520 2033 3629 0a2a (line 36).*\n+00020e40: 2064 7261 7761 626c 653a 2020 2020 2020 drawable: \n 00020e50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020e60: 2020 2020 2020 2020 2020 4f62 6a65 6374 Object\n-00020e70: 2074 7261 6e73 666f 726d 732e 2020 2028 transforms. (\n-00020e80: 6c69 6e65 2020 3237 290a 2a20 6472 6177 line 27).* draw\n-00020e90: 6162 6c65 203c 313e 3a20 2020 2020 2020 able <1>: \n+00020e60: 2020 2020 2020 2020 4f62 6a65 6374 2074 Object t\n+00020e70: 7261 6e73 666f 726d 732e 2020 2028 6c69 ransforms. (li\n+00020e80: 6e65 2020 3237 290a 2a20 6472 6177 6162 ne 27).* drawab\n+00020e90: 6c65 203c 313e 3a20 2020 2020 2020 2020 le <1>: \n 00020ea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020eb0: 2020 2044 7261 7761 626c 6573 2e20 2020 Drawables. \n-00020ec0: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n-00020ed0: 3629 0a2a 2064 7261 7761 626c 6520 6465 6).* drawable de\n-00020ee0: 6669 6e69 7469 6f6e 3a20 2020 2020 2020 finition: \n-00020ef0: 2020 2020 2020 2020 2020 2020 4f62 6a65 Obje\n-00020f00: 6374 2074 7261 6e73 666f 726d 732e 2020 ct transforms. \n-00020f10: 2028 6c69 6e65 2020 3237 290a 2a20 6472 (line 27).* dr\n-00020f20: 6177 6162 6c65 2072 6566 6572 656e 6365 awable reference\n-00020f30: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00020f40: 2020 2020 2046 6f72 6d73 206f 6620 7265 Forms of re\n-00020f50: 6665 7265 6e63 6573 2e20 286c 696e 6520 ferences. (line \n-00020f60: 2031 3729 0a2a 2065 6e64 2070 6f6c 7967 17).* end polyg\n-00020f70: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n-00020f80: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-00020f90: 6570 7420 6c69 6e65 732e 2020 2020 2020 ept lines. \n-00020fa0: 2020 2028 6c69 6e65 2020 3338 290a 2a20 (line 38).* \n-00020fb0: 656e 6420 706f 6c79 676f 6e20 3c31 3e3a end polygon <1>:\n+00020eb0: 2044 7261 7761 626c 6573 2e20 2020 2020 Drawables. \n+00020ec0: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n+00020ed0: 0a2a 2064 7261 7761 626c 6520 6465 6669 .* drawable defi\n+00020ee0: 6e69 7469 6f6e 3a20 2020 2020 2020 2020 nition: \n+00020ef0: 2020 2020 2020 2020 2020 4f62 6a65 6374 Object\n+00020f00: 2074 7261 6e73 666f 726d 732e 2020 2028 transforms. (\n+00020f10: 6c69 6e65 2020 3237 290a 2a20 6472 6177 line 27).* draw\n+00020f20: 6162 6c65 2072 6566 6572 656e 6365 3a20 able reference: \n+00020f30: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00020f40: 2020 2046 6f72 6d73 206f 6620 7265 6665 Forms of refe\n+00020f50: 7265 6e63 6573 2e20 286c 696e 6520 2031 rences. (line 1\n+00020f60: 3729 0a2a 2065 6e64 2070 6f6c 7967 6f6e 7).* end polygon\n+00020f70: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00020f80: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+00020f90: 7420 6c69 6e65 732e 2020 2020 2020 2020 t lines. \n+00020fa0: 2028 6c69 6e65 2020 3338 290a 2a20 656e (line 38).* en\n+00020fb0: 6420 706f 6c79 676f 6e20 3c31 3e3a 2020 d polygon <1>: \n 00020fc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00020fd0: 2020 2020 2020 2053 7765 7074 2070 6f6c Swept pol\n-00020fe0: 7967 6f6e 732e 2020 2020 2020 286c 696e ygons. (lin\n-00020ff0: 6520 2031 3529 0a2a 2066 6163 6573 3a20 e 15).* faces: \n+00020fd0: 2020 2020 2053 7765 7074 2070 6f6c 7967 Swept polyg\n+00020fe0: 6f6e 732e 2020 2020 2020 286c 696e 6520 ons. (line \n+00020ff0: 2031 3529 0a2a 2066 6163 6573 3a20 2020 15).* faces: \n 00021000: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021010: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021020: 4472 6177 696e 6720 6120 736f 6c69 642e Drawing a solid.\n-00021030: 2020 2020 2028 6c69 6e65 2020 2037 290a (line 7).\n-00021040: 2a20 6661 6365 7320 3c31 3e3a 2020 2020 * faces <1>: \n+00021010: 2020 2020 2020 2020 2020 2020 2020 4472 Dr\n+00021020: 6177 696e 6720 6120 736f 6c69 642e 2020 awing a solid. \n+00021030: 2020 2028 6c69 6e65 2020 2037 290a 2a20 (line 7).* \n+00021040: 6661 6365 7320 3c31 3e3a 2020 2020 2020 faces <1>: \n 00021050: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021060: 2020 2020 2020 2020 2050 6f6c 796c 696e Polylin\n-00021070: 6520 7377 6565 7073 2e20 2020 2020 286c e sweeps. (l\n-00021080: 696e 6520 2020 3629 0a2a 2066 696c 652c ine 6).* file,\n-00021090: 2069 6e63 6c75 6465 3a20 2020 2020 2020 include: \n+00021060: 2020 2020 2020 2050 6f6c 796c 696e 6520 Polyline \n+00021070: 7377 6565 7073 2e20 2020 2020 286c 696e sweeps. (lin\n+00021080: 6520 2020 3629 0a2a 2066 696c 652c 2069 e 6).* file, i\n+00021090: 6e63 6c75 6465 3a20 2020 2020 2020 2020 nclude: \n 000210a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000210b0: 2020 4c61 6e67 7561 6765 2062 6173 6963 Language basic\n-000210c0: 732e 2020 2020 2028 6c69 6e65 2020 3139 s. (line 19\n-000210d0: 290a 2a20 6669 6c65 2c20 696e 7075 743a ).* file, input:\n+000210b0: 4c61 6e67 7561 6765 2062 6173 6963 732e Language basics.\n+000210c0: 2020 2020 2028 6c69 6e65 2020 3139 290a (line 19).\n+000210d0: 2a20 6669 6c65 2c20 696e 7075 743a 2020 * file, input: \n 000210e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000210f0: 2020 2020 2020 2020 2020 204c 616e 6775 Langu\n-00021100: 6167 6520 6261 7369 6373 2e20 2020 2020 age basics. \n-00021110: 286c 696e 6520 2020 3629 0a2a 2066 7261 (line 6).* fra\n-00021120: 6d65 2062 6f78 3a20 2020 2020 2020 2020 me box: \n+000210f0: 2020 2020 2020 2020 204c 616e 6775 6167 Languag\n+00021100: 6520 6261 7369 6373 2e20 2020 2020 286c e basics. (l\n+00021110: 696e 6520 2020 3629 0a2a 2066 7261 6d65 ine 6).* frame\n+00021120: 2062 6f78 3a20 2020 2020 2020 2020 2020 box: \n 00021130: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021140: 2020 2020 4672 616d 652e 2020 2020 2020 Frame. \n-00021150: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00021160: 2036 290a 2a20 676c 6f62 616c 206f 7074 6).* global opt\n-00021170: 696f 6e73 3a20 2020 2020 2020 2020 2020 ions: \n-00021180: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n-00021190: 7769 6e67 206f 7074 696f 6e73 2e20 2020 wing options. \n-000211a0: 2020 286c 696e 6520 2031 3829 0a2a 2067 (line 18).* g\n-000211b0: 6c6f 6261 6c20 6f70 7469 6f6e 7320 3c31 lobal options <1\n-000211c0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-000211d0: 2020 2020 2020 476c 6f62 616c 206f 7074 Global opt\n-000211e0: 696f 6e73 2e20 2020 2020 2028 6c69 6e65 ions. (line\n-000211f0: 2020 2036 290a 2a20 6865 6c69 783a 2020 6).* helix: \n+00021140: 2020 4672 616d 652e 2020 2020 2020 2020 Frame. \n+00021150: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+00021160: 290a 2a20 676c 6f62 616c 206f 7074 696f ).* global optio\n+00021170: 6e73 3a20 2020 2020 2020 2020 2020 2020 ns: \n+00021180: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+00021190: 6e67 206f 7074 696f 6e73 2e20 2020 2020 ng options. \n+000211a0: 286c 696e 6520 2031 3829 0a2a 2067 6c6f (line 18).* glo\n+000211b0: 6261 6c20 6f70 7469 6f6e 7320 3c31 3e3a bal options <1>:\n+000211c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000211d0: 2020 2020 476c 6f62 616c 206f 7074 696f Global optio\n+000211e0: 6e73 2e20 2020 2020 2028 6c69 6e65 2020 ns. (line \n+000211f0: 2036 290a 2a20 6865 6c69 783a 2020 2020 6).* helix: \n 00021200: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021210: 2020 2020 2020 2020 2020 2020 2020 2044 D\n-00021220: 7261 7769 6e67 2061 2073 6f6c 6964 2e20 rawing a solid. \n-00021230: 2020 2020 286c 696e 6520 2034 3729 0a2a (line 47).*\n-00021240: 2068 656c 6978 203c 313e 3a20 2020 2020 helix <1>: \n+00021210: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n+00021220: 7769 6e67 2061 2073 6f6c 6964 2e20 2020 wing a solid. \n+00021230: 2020 286c 696e 6520 2034 3729 0a2a 2068 (line 47).* h\n+00021240: 656c 6978 203c 313e 3a20 2020 2020 2020 elix <1>: \n 00021250: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021260: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n-00021270: 2073 7765 6570 732e 2020 2020 2028 6c69 sweeps. (li\n-00021280: 6e65 2020 3135 290a 2a20 6865 6c6c 6f20 ne 15).* hello \n-00021290: 776f 726c 643a 2020 2020 2020 2020 2020 world: \n-000212a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000212b0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n-000212c0: 2020 2020 2020 286c 696e 6520 2020 3729 (line 7)\n-000212d0: 0a2a 2068 6964 6465 6e20 7375 7266 6163 .* hidden surfac\n-000212e0: 6520 616c 676f 7269 7468 6d3a 2020 2020 e algorithm: \n-000212f0: 2020 2020 2020 2020 2020 4865 6c6c 6f20 Hello \n-00021300: 776f 726c 642e 2020 2020 2020 2020 2028 world. (\n-00021310: 6c69 6e65 2020 3139 290a 2a20 6869 6464 line 19).* hidd\n-00021320: 656e 2073 7572 6661 6365 2061 6c67 6f72 en surface algor\n-00021330: 6974 686d 203c 313e 3a20 2020 2020 2020 ithm <1>: \n-00021340: 2020 2053 7065 6369 616c 206f 626a 6563 Special objec\n-00021350: 7473 2e20 2020 2020 286c 696e 6520 2034 ts. (line 4\n-00021360: 3829 0a2a 2068 6964 6465 6e20 7375 7266 8).* hidden surf\n-00021370: 6163 6520 616c 676f 7269 7468 6d20 3c32 ace algorithm <2\n-00021380: 3e3a 2020 2020 2020 2020 2020 5472 616e >: Tran\n-00021390: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-000213a0: 2028 6c69 6e65 2020 3234 290a 2a20 6869 (line 24).* hi\n-000213b0: 6464 656e 2073 7572 6661 6365 2061 6c67 dden surface alg\n-000213c0: 6f72 6974 686d 203c 333e 3a20 2020 2020 orithm <3>: \n-000213d0: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n-000213e0: 2064 7261 7769 6e67 2e20 286c 696e 6520 drawing. (line \n-000213f0: 2032 3529 0a2a 2068 6964 6465 6e20 7375 25).* hidden su\n-00021400: 7266 6163 6520 616c 676f 7269 7468 6d20 rface algorithm \n-00021410: 3c34 3e3a 2020 2020 2020 2020 2020 4869 <4>: Hi\n-00021420: 6464 656e 2073 7572 6661 6365 2072 656d dden surface rem\n-00021430: 6f76 616c 2e0a 2020 2020 2020 2020 2020 oval.. \n+00021260: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n+00021270: 7765 6570 732e 2020 2020 2028 6c69 6e65 weeps. (line\n+00021280: 2020 3135 290a 2a20 6865 6c6c 6f20 776f 15).* hello wo\n+00021290: 726c 643a 2020 2020 2020 2020 2020 2020 rld: \n+000212a0: 2020 2020 2020 2020 2020 2020 2020 2048 H\n+000212b0: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020 ello world. \n+000212c0: 2020 2020 286c 696e 6520 2020 3729 0a2a (line 7).*\n+000212d0: 2068 6964 6465 6e20 7375 7266 6163 6520 hidden surface \n+000212e0: 616c 676f 7269 7468 6d3a 2020 2020 2020 algorithm: \n+000212f0: 2020 2020 2020 2020 4865 6c6c 6f20 776f Hello wo\n+00021300: 726c 642e 2020 2020 2020 2020 2028 6c69 rld. (li\n+00021310: 6e65 2020 3139 290a 2a20 6869 6464 656e ne 19).* hidden\n+00021320: 2073 7572 6661 6365 2061 6c67 6f72 6974 surface algorit\n+00021330: 686d 203c 313e 3a20 2020 2020 2020 2020 hm <1>: \n+00021340: 2053 7065 6369 616c 206f 626a 6563 7473 Special objects\n+00021350: 2e20 2020 2020 286c 696e 6520 2034 3829 . (line 48)\n+00021360: 0a2a 2068 6964 6465 6e20 7375 7266 6163 .* hidden surfac\n+00021370: 6520 616c 676f 7269 7468 6d20 3c32 3e3a e algorithm <2>:\n+00021380: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+00021390: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028 orm literals. (\n+000213a0: 6c69 6e65 2020 3234 290a 2a20 6869 6464 line 24).* hidd\n+000213b0: 656e 2073 7572 6661 6365 2061 6c67 6f72 en surface algor\n+000213c0: 6974 686d 203c 333e 3a20 2020 2020 2020 ithm <3>: \n+000213d0: 2020 2041 2074 6563 686e 6963 616c 2064 A technical d\n+000213e0: 7261 7769 6e67 2e20 286c 696e 6520 2032 rawing. (line 2\n+000213f0: 3529 0a2a 2068 6964 6465 6e20 7375 7266 5).* hidden surf\n+00021400: 6163 6520 616c 676f 7269 7468 6d20 3c34 ace algorithm <4\n+00021410: 3e3a 2020 2020 2020 2020 2020 4869 6464 >: Hidd\n+00021420: 656e 2073 7572 6661 6365 2072 656d 6f76 en surface remov\n+00021430: 616c 2e0a 2020 2020 2020 2020 2020 2020 al.. \n 00021440: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021450: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021460: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021470: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n-00021480: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-00021490: 6465 6c3a 2020 2020 2020 2020 2020 2020 del: \n-000214a0: 2020 2020 2020 2020 4120 6869 6572 6172 A hierar\n-000214b0: 6368 6963 616c 206d 6f64 656c 2e0a 2020 chical model.. \n+00021470: 2020 286c 696e 6520 2020 3629 0a2a 2068 (line 6).* h\n+00021480: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+00021490: 6c3a 2020 2020 2020 2020 2020 2020 2020 l: \n+000214a0: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n+000214b0: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n 000214c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000214d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000214e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000214f0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-00021500: 6520 2020 3629 0a2a 2069 6465 6e74 6966 e 6).* identif\n-00021510: 6965 7273 3a20 2020 2020 2020 2020 2020 iers: \n-00021520: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021530: 4964 656e 7469 6669 6572 732e 2020 2020 Identifiers. \n-00021540: 2020 2020 2028 6c69 6e65 2020 2037 290a (line 7).\n-00021550: 2a20 696e 636c 7564 6520 6669 6c65 3a20 * include file: \n+000214f0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+00021500: 2020 3629 0a2a 2069 6465 6e74 6966 6965 6).* identifie\n+00021510: 7273 3a20 2020 2020 2020 2020 2020 2020 rs: \n+00021520: 2020 2020 2020 2020 2020 2020 2020 4964 Id\n+00021530: 656e 7469 6669 6572 732e 2020 2020 2020 entifiers. \n+00021540: 2020 2028 6c69 6e65 2020 2037 290a 2a20 (line 7).* \n+00021550: 696e 636c 7564 6520 6669 6c65 3a20 2020 include file: \n 00021560: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021570: 2020 2020 2020 2020 204c 616e 6775 6167 Languag\n-00021580: 6520 6261 7369 6373 2e20 2020 2020 286c e basics. (l\n-00021590: 696e 6520 2031 3929 0a2a 2069 6e70 7574 ine 19).* input\n-000215a0: 2066 696c 653a 2020 2020 2020 2020 2020 file: \n+00021570: 2020 2020 2020 204c 616e 6775 6167 6520 Language \n+00021580: 6261 7369 6373 2e20 2020 2020 286c 696e basics. (lin\n+00021590: 6520 2031 3929 0a2a 2069 6e70 7574 2066 e 19).* input f\n+000215a0: 696c 653a 2020 2020 2020 2020 2020 2020 ile: \n 000215b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000215c0: 2020 4c61 6e67 7561 6765 2062 6173 6963 Language basic\n-000215d0: 732e 2020 2020 2028 6c69 6e65 2020 2036 s. (line 6\n-000215e0: 290a 2a20 696e 7465 726e 616c 206f 7074 ).* internal opt\n-000215f0: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n-00021600: 2020 2020 2020 2020 2020 2053 7065 6369 Speci\n-00021610: 616c 206f 626a 6563 7473 2e20 2020 2020 al objects. \n-00021620: 286c 696e 6520 2034 3729 0a2a 2069 6e74 (line 47).* int\n-00021630: 6572 6e61 6c20 6f70 7469 6f6e 733a 2020 ernal options: \n+000215c0: 4c61 6e67 7561 6765 2062 6173 6963 732e Language basics.\n+000215d0: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+000215e0: 2a20 696e 7465 726e 616c 206f 7074 696f * internal optio\n+000215f0: 6e3a 2020 2020 2020 2020 2020 2020 2020 n: \n+00021600: 2020 2020 2020 2020 2053 7065 6369 616c Special\n+00021610: 206f 626a 6563 7473 2e20 2020 2020 286c objects. (l\n+00021620: 696e 6520 2034 3729 0a2a 2069 6e74 6572 ine 47).* inter\n+00021630: 6e61 6c20 6f70 7469 6f6e 733a 2020 2020 nal options: \n 00021640: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021650: 2020 2020 496e 7465 726e 616c 206f 7074 Internal opt\n-00021660: 696f 6e73 2e20 2020 2028 6c69 6e65 2020 ions. (line \n-00021670: 2036 290a 2a20 696e 7465 726e 616c 206f 6).* internal o\n-00021680: 7074 696f 6e73 203c 313e 3a20 2020 2020 ptions <1>: \n-00021690: 2020 2020 2020 2020 2020 2020 2047 6c6f Glo\n-000216a0: 6261 6c20 6f70 7469 6f6e 732e 2020 2020 bal options. \n-000216b0: 2020 286c 696e 6520 2031 3229 0a2a 206b (line 12).* k\n-000216c0: 6579 776f 7264 733a 2020 2020 2020 2020 eywords: \n+00021650: 2020 496e 7465 726e 616c 206f 7074 696f Internal optio\n+00021660: 6e73 2e20 2020 2028 6c69 6e65 2020 2036 ns. 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(l\n-000217d0: 696e 6520 2020 3829 0a2a 206c 616e 6775 ine 8).* langu\n-000217e0: 6167 652c 206f 7574 7075 743a 2020 2020 age, output: \n+00021760: 2020 2020 2020 2020 2020 2020 2020 5370 Sp\n+00021770: 6563 6961 6c20 6f62 6a65 6374 732e 2020 ecial objects. \n+00021780: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n+00021790: 6c61 6e67 7561 6765 2c20 6465 636c 6172 language, declar\n+000217a0: 6174 6976 653a 2020 2020 2020 2020 2020 ative: \n+000217b0: 2020 2020 2020 204c 616e 6775 6167 6520 Language \n+000217c0: 6261 7369 6373 2e20 2020 2020 286c 696e basics. 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(l\n+00021860: 696e 6520 2020 3829 0a2a 206c 6578 6963 ine 8).* lexic\n+00021870: 616c 2073 636f 7065 3a20 2020 2020 2020 al scope: \n 00021880: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021890: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n-000218a0: 666f 726d 732e 2020 2028 6c69 6e65 2020 forms. (line \n-000218b0: 3236 290a 2a20 6c65 7869 6361 6c20 7363 26).* lexical sc\n-000218c0: 6f70 6520 3c31 3e3a 2020 2020 2020 2020 ope <1>: \n-000218d0: 2020 2020 2020 2020 2020 2020 2042 6c6f Blo\n-000218e0: 636b 732e 2020 2020 2020 2020 2020 2020 cks. \n-000218f0: 2020 286c 696e 6520 2031 3329 0a2a 206c (line 13).* l\n-00021900: 696e 6520 7377 6565 703a 2020 2020 2020 ine sweep: \n+00021890: 2020 4f62 6a65 6374 2074 7261 6e73 666f Object transfo\n+000218a0: 726d 732e 2020 2028 6c69 6e65 2020 3236 rms. (line 26\n+000218b0: 290a 2a20 6c65 7869 6361 6c20 7363 6f70 ).* lexical scop\n+000218c0: 6520 3c31 3e3a 2020 2020 2020 2020 2020 e <1>: \n+000218d0: 2020 2020 2020 2020 2020 2042 6c6f 636b Block\n+000218e0: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n+000218f0: 286c 696e 6520 2031 3329 0a2a 206c 696e (line 13).* lin\n+00021900: 6520 7377 6565 703a 2020 2020 2020 2020 e sweep: \n 00021910: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021920: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n-00021930: 7765 6570 732e 2020 2020 2028 6c69 6e65 weeps. (line\n-00021940: 2020 2036 290a 2a20 6c69 6e65 2073 7765 6).* line swe\n-00021950: 6570 203c 313e 3a20 2020 2020 2020 2020 ep <1>: \n-00021960: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-00021970: 7765 7074 206c 696e 6573 2e20 2020 2020 wept lines. \n-00021980: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n-00021990: 206c 696e 6520 7377 6565 7020 3c32 3e3a line sweep <2>:\n+00021920: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n+00021930: 6570 732e 2020 2020 2028 6c69 6e65 2020 eps. (line \n+00021940: 2036 290a 2a20 6c69 6e65 2073 7765 6570 6).* line sweep\n+00021950: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00021960: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00021970: 7074 206c 696e 6573 2e20 2020 2020 2020 pt lines. \n+00021980: 2020 286c 696e 6520 2020 3629 0a2a 206c (line 6).* l\n+00021990: 696e 6520 7377 6565 7020 3c32 3e3a 2020 ine sweep <2>: \n 000219a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000219b0: 2020 2020 2020 2020 4120 7465 6368 6e69 A techni\n-000219c0: 6361 6c20 6472 6177 696e 672e 2028 6c69 cal drawing. (li\n-000219d0: 6e65 2020 3230 290a 2a20 6c69 7465 7261 ne 20).* litera\n-000219e0: 6c2c 2070 6f69 6e74 3a20 2020 2020 2020 l, point: \n-000219f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021a00: 2050 6f69 6e74 2061 6e64 2076 6563 746f Point and vecto\n-00021a10: 7220 6c69 7465 7261 6c73 2e0a 2020 2020 r literals.. \n+000219b0: 2020 2020 2020 4120 7465 6368 6e69 6361 A technica\n+000219c0: 6c20 6472 6177 696e 672e 2028 6c69 6e65 l drawing. (line\n+000219d0: 2020 3230 290a 2a20 6c69 7465 7261 6c2c 20).* literal,\n+000219e0: 2070 6f69 6e74 3a20 2020 2020 2020 2020 point: \n+000219f0: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+00021a00: 6f69 6e74 2061 6e64 2076 6563 746f 7220 oint and vector \n+00021a10: 6c69 7465 7261 6c73 2e0a 2020 2020 2020 literals.. \n 00021a20: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021a30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021a40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021a50: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-00021a60: 2020 3629 0a2a 206c 6974 6572 616c 2c20 6).* literal, \n-00021a70: 7363 616c 6172 3a20 2020 2020 2020 2020 scalar: \n-00021a80: 2020 2020 2020 2020 2020 2020 2020 5363 Sc\n-00021a90: 616c 6172 206c 6974 6572 616c 732e 2020 alar literals. \n-00021aa0: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n-00021ab0: 6c69 7465 7261 6c2c 2074 7261 6e73 666f literal, transfo\n-00021ac0: 726d 3a20 2020 2020 2020 2020 2020 2020 rm: \n-00021ad0: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-00021ae0: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-00021af0: 6520 2020 3629 0a2a 206c 6974 6572 616c e 6).* literal\n-00021b00: 2c20 7665 6374 6f72 3a20 2020 2020 2020 , vector: \n-00021b10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021b20: 506f 696e 7420 616e 6420 7665 6374 6f72 Point and vector\n-00021b30: 206c 6974 6572 616c 732e 0a20 2020 2020 literals.. \n+00021a50: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+00021a60: 3629 0a2a 206c 6974 6572 616c 2c20 7363 6).* literal, sc\n+00021a70: 616c 6172 3a20 2020 2020 2020 2020 2020 alar: \n+00021a80: 2020 2020 2020 2020 2020 2020 5363 616c Scal\n+00021a90: 6172 206c 6974 6572 616c 732e 2020 2020 ar literals. \n+00021aa0: 2028 6c69 6e65 2020 2036 290a 2a20 6c69 (line 6).* li\n+00021ab0: 7465 7261 6c2c 2074 7261 6e73 666f 726d teral, transform\n+00021ac0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00021ad0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+00021ae0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+00021af0: 2020 3629 0a2a 206c 6974 6572 616c 2c20 6).* literal, \n+00021b00: 7665 6374 6f72 3a20 2020 2020 2020 2020 vector: \n+00021b10: 2020 2020 2020 2020 2020 2020 2020 506f Po\n+00021b20: 696e 7420 616e 6420 7665 6374 6f72 206c int and vector l\n+00021b30: 6974 6572 616c 732e 0a20 2020 2020 2020 iterals.. \n 00021b40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021b50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021b60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021b70: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00021b80: 2036 290a 2a20 6e65 7374 696e 672c 2073 6).* nesting, s\n-00021b90: 7765 7074 206f 626a 6563 743a 2020 2020 wept object: \n-00021ba0: 2020 2020 2020 2020 2020 2020 204e 6573 Nes\n-00021bb0: 7465 6420 7377 6565 7073 2e20 2020 2020 ted sweeps. \n-00021bc0: 2020 286c 696e 6520 2032 3229 0a2a 206f (line 22).* o\n-00021bd0: 6e65 2d6f 7065 7261 6e64 2066 6f72 6d3a ne-operand form:\n+00021b70: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n+00021b80: 290a 2a20 6e65 7374 696e 672c 2073 7765 ).* nesting, swe\n+00021b90: 7074 206f 626a 6563 743a 2020 2020 2020 pt object: \n+00021ba0: 2020 2020 2020 2020 2020 204e 6573 7465 Neste\n+00021bb0: 6420 7377 6565 7073 2e20 2020 2020 2020 d sweeps. \n+00021bc0: 286c 696e 6520 2032 3229 0a2a 206f 6e65 (line 22).* one\n+00021bd0: 2d6f 7065 7261 6e64 2066 6f72 6d3a 2020 -operand form: \n 00021be0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021bf0: 2020 2020 2020 556e 6172 7920 666f 726d Unary form\n-00021c00: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-00021c10: 2020 2036 290a 2a20 6f70 6572 6174 6f72 6).* operator\n-00021c20: 2061 7373 6f63 6961 7469 7669 7479 3a20 associativity: \n-00021c30: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-00021c40: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n-00021c50: 7279 2920 666f 726d 732e 0a20 2020 2020 ry) forms.. \n+00021bf0: 2020 2020 556e 6172 7920 666f 726d 732e Unary forms.\n+00021c00: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00021c10: 2036 290a 2a20 6f70 6572 6174 6f72 2061 6).* operator a\n+00021c20: 7373 6f63 6961 7469 7669 7479 3a20 2020 ssociativity: \n+00021c30: 2020 2020 2020 2020 2020 2020 2054 776f Two\n+00021c40: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n+00021c50: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n 00021c60: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021c70: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021c80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021c90: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00021ca0: 3538 290a 2a20 6f70 6572 6174 6f72 2070 58).* operator p\n-00021cb0: 7265 6365 6465 6e63 653a 2020 2020 2020 recedence: \n-00021cc0: 2020 2020 2020 2020 2020 2020 2054 776f Two\n-00021cd0: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n-00021ce0: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n+00021c90: 2020 2020 2020 2028 6c69 6e65 2020 3538 (line 58\n+00021ca0: 290a 2a20 6f70 6572 6174 6f72 2070 7265 ).* operator pre\n+00021cb0: 6365 6465 6e63 653a 2020 2020 2020 2020 cedence: \n+00021cc0: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n+00021cd0: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n+00021ce0: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n 00021cf0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021d00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021d10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021d20: 2020 2020 2020 2028 6c69 6e65 2020 3435 (line 45\n-00021d30: 290a 2a20 6f70 7469 6f6e 3a20 2020 2020 ).* option: \n+00021d20: 2020 2020 2028 6c69 6e65 2020 3435 290a (line 45).\n+00021d30: 2a20 6f70 7469 6f6e 3a20 2020 2020 2020 * option: \n 00021d40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021d50: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n-00021d60: 6e67 206f 7074 696f 6e73 2e20 2020 2020 ng options. \n-00021d70: 286c 696e 6520 2020 3629 0a2a 206f 7074 (line 6).* opt\n-00021d80: 696f 6e2c 2063 6f6d 6d61 6e64 206c 696e ion, command lin\n-00021d90: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-00021da0: 2020 2020 4865 6c6c 6f20 776f 726c 642e Hello world.\n-00021db0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00021dc0: 3330 290a 2a20 6f70 7469 6f6e 2c20 696e 30).* option, in\n-00021dd0: 7465 726e 616c 3a20 2020 2020 2020 2020 ternal: \n-00021de0: 2020 2020 2020 2020 2020 2020 2053 7065 Spe\n-00021df0: 6369 616c 206f 626a 6563 7473 2e20 2020 cial objects. \n-00021e00: 2020 286c 696e 6520 2034 3729 0a2a 206f (line 47).* o\n-00021e10: 7074 696f 6e73 3a20 2020 2020 2020 2020 ptions: \n+00021d50: 2020 2020 2020 2020 2044 7261 7769 6e67 Drawing\n+00021d60: 206f 7074 696f 6e73 2e20 2020 2020 286c options. (l\n+00021d70: 696e 6520 2020 3629 0a2a 206f 7074 696f ine 6).* optio\n+00021d80: 6e2c 2063 6f6d 6d61 6e64 206c 696e 653a n, command line:\n+00021d90: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00021da0: 2020 4865 6c6c 6f20 776f 726c 642e 2020 Hello world. \n+00021db0: 2020 2020 2020 2028 6c69 6e65 2020 3330 (line 30\n+00021dc0: 290a 2a20 6f70 7469 6f6e 2c20 696e 7465 ).* option, inte\n+00021dd0: 726e 616c 3a20 2020 2020 2020 2020 2020 rnal: \n+00021de0: 2020 2020 2020 2020 2020 2053 7065 6369 Speci\n+00021df0: 616c 206f 626a 6563 7473 2e20 2020 2020 al objects. \n+00021e00: 286c 696e 6520 2034 3729 0a2a 206f 7074 (line 47).* opt\n+00021e10: 696f 6e73 3a20 2020 2020 2020 2020 2020 ions: \n 00021e20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021e30: 2020 2020 2020 4f70 7469 6f6e 732e 2020 Options. \n-00021e40: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00021e50: 2020 2036 290a 2a20 6f70 7469 6f6e 7320 6).* options \n-00021e60: 6465 6669 6e69 7469 6f6e 3a20 2020 2020 definition: \n-00021e70: 2020 2020 2020 2020 2020 2020 2020 2050 P\n-00021e80: 6f6c 796c 696e 6520 7377 6565 7073 2077 olyline sweeps w\n-00021e90: 6974 6820 636c 6f73 7572 652e 0a20 2020 ith closure.. \n+00021e30: 2020 2020 4f70 7469 6f6e 732e 2020 2020 Options. \n+00021e40: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00021e50: 2036 290a 2a20 6f70 7469 6f6e 7320 6465 6).* options de\n+00021e60: 6669 6e69 7469 6f6e 3a20 2020 2020 2020 finition: \n+00021e70: 2020 2020 2020 2020 2020 2020 2050 6f6c Pol\n+00021e80: 796c 696e 6520 7377 6565 7073 2077 6974 yline sweeps wit\n+00021e90: 6820 636c 6f73 7572 652e 0a20 2020 2020 h closure.. \n 00021ea0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021eb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00021ec0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021ed0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00021ee0: 2020 3233 290a 2a20 6f70 7469 6f6e 7320 23).* options \n-00021ef0: 6d75 6c74 6970 6c65 2072 6566 6572 656e multiple referen\n-00021f00: 6365 3a20 2020 2020 2020 2020 2020 2046 ce: F\n-00021f10: 6f72 6d73 206f 6620 7265 6665 7265 6e63 orms of referenc\n-00021f20: 6573 2e20 286c 696e 6520 2031 3829 0a2a es. (line 18).*\n-00021f30: 206f 7074 696f 6e73 2072 6566 6572 656e options referen\n-00021f40: 6365 3a20 2020 2020 2020 2020 2020 2020 ce: \n-00021f50: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n-00021f60: 2072 6566 6572 656e 6365 732e 2028 6c69 references. (li\n-00021f70: 6e65 2020 3138 290a 2a20 6f70 7469 6f6e ne 18).* option\n-00021f80: 732c 2063 6f6d 6d61 6e64 206c 696e 653a s, command line:\n-00021f90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00021fa0: 2043 6f6d 6d61 6e64 206c 696e 652e 2020 Command line. \n-00021fb0: 2020 2020 2020 286c 696e 6520 2031 3429 (line 14)\n-00021fc0: 0a2a 206f 7074 696f 6e73 2c20 676c 6f62 .* options, glob\n-00021fd0: 616c 3a20 2020 2020 2020 2020 2020 2020 al: \n-00021fe0: 2020 2020 2020 2020 2020 4472 6177 696e Drawin\n-00021ff0: 6720 6f70 7469 6f6e 732e 2020 2020 2028 g options. (\n-00022000: 6c69 6e65 2020 3138 290a 2a20 6f70 7469 line 18).* opti\n-00022010: 6f6e 732c 2067 6c6f 6261 6c20 3c31 3e3a ons, global <1>:\n+00021ed0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00021ee0: 3233 290a 2a20 6f70 7469 6f6e 7320 6d75 23).* options mu\n+00021ef0: 6c74 6970 6c65 2072 6566 6572 656e 6365 ltiple reference\n+00021f00: 3a20 2020 2020 2020 2020 2020 2046 6f72 : For\n+00021f10: 6d73 206f 6620 7265 6665 7265 6e63 6573 ms of references\n+00021f20: 2e20 286c 696e 6520 2031 3829 0a2a 206f . (line 18).* o\n+00021f30: 7074 696f 6e73 2072 6566 6572 656e 6365 ptions reference\n+00021f40: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00021f50: 2020 2020 2020 466f 726d 7320 6f66 2072 Forms of r\n+00021f60: 6566 6572 656e 6365 732e 2028 6c69 6e65 eferences. (line\n+00021f70: 2020 3138 290a 2a20 6f70 7469 6f6e 732c 18).* options,\n+00021f80: 2063 6f6d 6d61 6e64 206c 696e 653a 2020 command line: \n+00021f90: 2020 2020 2020 2020 2020 2020 2020 2043 C\n+00021fa0: 6f6d 6d61 6e64 206c 696e 652e 2020 2020 ommand line. \n+00021fb0: 2020 2020 286c 696e 6520 2031 3429 0a2a (line 14).*\n+00021fc0: 206f 7074 696f 6e73 2c20 676c 6f62 616c options, global\n+00021fd0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00021fe0: 2020 2020 2020 2020 4472 6177 696e 6720 Drawing \n+00021ff0: 6f70 7469 6f6e 732e 2020 2020 2028 6c69 options. (li\n+00022000: 6e65 2020 3138 290a 2a20 6f70 7469 6f6e ne 18).* option\n+00022010: 732c 2067 6c6f 6261 6c20 3c31 3e3a 2020 s, global <1>: \n 00022020: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022030: 2020 2047 6c6f 6261 6c20 6f70 7469 6f6e Global option\n-00022040: 732e 2020 2020 2020 286c 696e 6520 2020 s. (line \n-00022050: 3629 0a2a 206f 7074 696f 6e73 2c20 696e 6).* options, in\n-00022060: 7465 726e 616c 3a20 2020 2020 2020 2020 ternal: \n-00022070: 2020 2020 2020 2020 2020 2020 496e 7465 Inte\n-00022080: 726e 616c 206f 7074 696f 6e73 2e20 2020 rnal options. \n-00022090: 2028 6c69 6e65 2020 2036 290a 2a20 6f70 (line 6).* op\n-000220a0: 7469 6f6e 732c 2069 6e74 6572 6e61 6c20 tions, internal \n-000220b0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-000220c0: 2020 2020 2047 6c6f 6261 6c20 6f70 7469 Global opti\n-000220d0: 6f6e 732e 2020 2020 2020 286c 696e 6520 ons. (line \n-000220e0: 2031 3229 0a2a 206f 7074 696f 6e73 2c20 12).* options, \n-000220f0: 7377 6565 703a 2020 2020 2020 2020 2020 sweep: \n-00022100: 2020 2020 2020 2020 2020 2020 2020 506f Po\n-00022110: 6c79 6c69 6e65 2073 7765 6570 732e 2020 lyline sweeps. \n-00022120: 2020 2028 6c69 6e65 2020 3136 290a 2a20 (line 16).* \n-00022130: 6f70 7469 6f6e 732c 2073 7765 6570 203c options, sweep <\n-00022140: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n-00022150: 2020 2020 2020 2050 6f6c 7967 6f6e 2073 Polygon s\n-00022160: 7765 6570 732e 2020 2020 2020 286c 696e weeps. (lin\n-00022170: 6520 2020 3929 0a2a 206f 7074 696f 6e73 e 9).* options\n-00022180: 2c20 7377 6565 7020 3c32 3e3a 2020 2020 , sweep <2>: \n-00022190: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000221a0: 5377 6570 7420 706f 696e 7473 2e20 2020 Swept points. \n-000221b0: 2020 2020 2028 6c69 6e65 2020 3231 290a (line 21).\n-000221c0: 2a20 6f70 7469 6f6e 732c 2073 7765 6570 * options, sweep\n-000221d0: 203c 333e 3a20 2020 2020 2020 2020 2020 <3>: \n-000221e0: 2020 2020 2020 2020 2053 7765 7074 206c Swept l\n-000221f0: 696e 6573 2e20 2020 2020 2020 2020 286c ines. (l\n-00022200: 696e 6520 2032 3529 0a2a 206f 7074 696f ine 25).* optio\n-00022210: 6e73 2c20 7377 6565 7020 3c34 3e3a 2020 ns, sweep <4>: \n+00022030: 2047 6c6f 6261 6c20 6f70 7469 6f6e 732e Global options.\n+00022040: 2020 2020 2020 286c 696e 6520 2020 3629 (line 6)\n+00022050: 0a2a 206f 7074 696f 6e73 2c20 696e 7465 .* options, inte\n+00022060: 726e 616c 3a20 2020 2020 2020 2020 2020 rnal: \n+00022070: 2020 2020 2020 2020 2020 496e 7465 726e Intern\n+00022080: 616c 206f 7074 696f 6e73 2e20 2020 2028 al options. (\n+00022090: 6c69 6e65 2020 2036 290a 2a20 6f70 7469 line 6).* opti\n+000220a0: 6f6e 732c 2069 6e74 6572 6e61 6c20 3c31 ons, internal <1\n+000220b0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+000220c0: 2020 2047 6c6f 6261 6c20 6f70 7469 6f6e Global option\n+000220d0: 732e 2020 2020 2020 286c 696e 6520 2031 s. (line 1\n+000220e0: 3229 0a2a 206f 7074 696f 6e73 2c20 7377 2).* options, sw\n+000220f0: 6565 703a 2020 2020 2020 2020 2020 2020 eep: \n+00022100: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n+00022110: 6c69 6e65 2073 7765 6570 732e 2020 2020 line sweeps. \n+00022120: 2028 6c69 6e65 2020 3136 290a 2a20 6f70 (line 16).* op\n+00022130: 7469 6f6e 732c 2073 7765 6570 203c 313e tions, sweep <1>\n+00022140: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00022150: 2020 2020 2050 6f6c 7967 6f6e 2073 7765 Polygon swe\n+00022160: 6570 732e 2020 2020 2020 286c 696e 6520 eps. (line \n+00022170: 2020 3929 0a2a 206f 7074 696f 6e73 2c20 9).* options, \n+00022180: 7377 6565 7020 3c32 3e3a 2020 2020 2020 sweep <2>: \n+00022190: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+000221a0: 6570 7420 706f 696e 7473 2e20 2020 2020 ept points. \n+000221b0: 2020 2028 6c69 6e65 2020 3231 290a 2a20 (line 21).* \n+000221c0: 6f70 7469 6f6e 732c 2073 7765 6570 203c options, sweep <\n+000221d0: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n+000221e0: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n+000221f0: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n+00022200: 6520 2032 3529 0a2a 206f 7074 696f 6e73 e 25).* options\n+00022210: 2c20 7377 6565 7020 3c34 3e3a 2020 2020 , sweep <4>: \n 00022220: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022230: 2020 5377 6570 7420 6c69 6e65 732e 2020 Swept lines. \n-00022240: 2020 2020 2020 2028 6c69 6e65 2020 3438 (line 48\n-00022250: 290a 2a20 6f70 7469 6f6e 732c 2073 7765 ).* options, swe\n-00022260: 7074 206f 626a 6563 743a 2020 2020 2020 pt object: \n-00022270: 2020 2020 2020 2020 2020 2050 6f6c 7967 Polyg\n-00022280: 6f6e 2073 7765 6570 732e 2020 2020 2020 on sweeps. \n-00022290: 286c 696e 6520 2020 3829 0a2a 206f 7074 (line 8).* opt\n-000222a0: 696f 6e73 2c20 7377 6570 7420 6f62 6a65 ions, swept obje\n-000222b0: 6374 203c 313e 3a20 2020 2020 2020 2020 ct <1>: \n-000222c0: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n-000222d0: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n-000222e0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00022230: 5377 6570 7420 6c69 6e65 732e 2020 2020 Swept lines. \n+00022240: 2020 2020 2028 6c69 6e65 2020 3438 290a (line 48).\n+00022250: 2a20 6f70 7469 6f6e 732c 2073 7765 7074 * options, swept\n+00022260: 206f 626a 6563 743a 2020 2020 2020 2020 object: \n+00022270: 2020 2020 2020 2020 2050 6f6c 7967 6f6e Polygon\n+00022280: 2073 7765 6570 732e 2020 2020 2020 286c sweeps. (l\n+00022290: 696e 6520 2020 3829 0a2a 206f 7074 696f ine 8).* optio\n+000222a0: 6e73 2c20 7377 6570 7420 6f62 6a65 6374 ns, swept object\n+000222b0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+000222c0: 2020 506f 6c79 6c69 6e65 2073 7765 6570 Polyline sweep\n+000222d0: 7320 7769 7468 2063 6c6f 7375 7265 2e0a s with closure..\n+000222e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000222f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022310: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022320: 286c 696e 6520 2032 3229 0a2a 206f 7074 (line 22).* opt\n-00022330: 696f 6e73 2c20 7377 6570 7420 6f62 6a65 ions, swept obje\n-00022340: 6374 203c 323e 3a20 2020 2020 2020 2020 ct <2>: \n-00022350: 2020 2020 5377 6570 7420 6c69 6e65 732e Swept lines.\n-00022360: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00022370: 3236 290a 2a20 6f70 7469 6f6e 732c 2073 26).* options, s\n-00022380: 7765 7074 206f 626a 6563 7420 3c33 3e3a wept object <3>:\n-00022390: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-000223a0: 7074 206c 696e 6573 2e20 2020 2020 2020 pt lines. \n-000223b0: 2020 286c 696e 6520 2034 3829 0a2a 206f (line 48).* o\n-000223c0: 7264 6572 2c20 706f 6c79 676f 6e20 7665 rder, polygon ve\n-000223d0: 7274 6578 3a20 2020 2020 2020 2020 2020 rtex: \n-000223e0: 2020 2020 2020 4865 6c6c 6f20 776f 726c Hello worl\n-000223f0: 642e 2020 2020 2020 2020 2028 6c69 6e65 d. (line\n-00022400: 2020 3339 290a 2a20 6f72 6465 722c 2070 39).* order, p\n-00022410: 6f6c 7967 6f6e 2076 6572 7465 7820 3c31 olygon vertex <1\n-00022420: 3e3a 2020 2020 2020 2020 2020 2020 2053 >: S\n-00022430: 7765 7074 206c 696e 6573 2e20 2020 2020 wept lines. \n-00022440: 2020 2020 286c 696e 6520 2031 3429 0a2a (line 14).*\n-00022450: 206f 7264 6572 2c20 706f 6c79 676f 6e20 order, polygon \n-00022460: 7665 7274 6578 203c 323e 3a20 2020 2020 vertex <2>: \n-00022470: 2020 2020 2020 2020 5377 6570 7420 6c69 Swept li\n-00022480: 6e65 732e 2020 2020 2020 2020 2028 6c69 nes. (li\n-00022490: 6e65 2020 3430 290a 2a20 6f72 6465 722c ne 40).* order,\n-000224a0: 2070 6f6c 7967 6f6e 2076 6572 7465 7820 polygon vertex \n-000224b0: 3c33 3e3a 2020 2020 2020 2020 2020 2020 <3>: \n-000224c0: 2053 7765 7074 2070 6f6c 7967 6f6e 732e Swept polygons.\n-000224d0: 2020 2020 2020 286c 696e 6520 2031 3929 (line 19)\n-000224e0: 0a2a 206f 7264 6572 2c20 706f 6c79 676f .* order, polygo\n-000224f0: 6e20 7665 7274 6578 203c 343e 3a20 2020 n vertex <4>: \n-00022500: 2020 2020 2020 2020 2020 4f76 6572 7669 Overvi\n-00022510: 6577 2e20 2020 2020 2020 2020 2020 2028 ew. (\n-00022520: 6c69 6e65 2020 3337 290a 2a20 6f72 6465 line 37).* orde\n-00022530: 722c 2070 6f6c 7967 6f6e 2076 6572 7465 r, polygon verte\n-00022540: 7820 3c35 3e3a 2020 2020 2020 2020 2020 x <5>: \n-00022550: 2020 204f 7665 7276 6965 772e 2020 2020 Overview. \n-00022560: 2020 2020 2020 2020 286c 696e 6520 2035 (line 5\n-00022570: 3529 0a2a 206f 7574 7075 7420 6c61 6e67 5).* output lang\n-00022580: 7561 6765 3a20 2020 2020 2020 2020 2020 uage: \n-00022590: 2020 2020 2020 2020 2020 2020 4c61 6e67 Lang\n-000225a0: 7561 6765 2e20 2020 2020 2020 2020 2020 uage. \n-000225b0: 2028 6c69 6e65 2020 2036 290a 2a20 6f75 (line 6).* ou\n-000225c0: 7473 6964 6520 6f66 2061 2070 6f6c 7967 tside of a polyg\n-000225d0: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n-000225e0: 2020 2020 2048 656c 6c6f 2077 6f72 6c64 Hello world\n-000225f0: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n-00022600: 2033 3729 0a2a 2070 6172 616c 6c65 6c20 37).* parallel \n-00022610: 7072 6f6a 6563 7469 6f6e 3a20 2020 2020 projection: \n-00022620: 2020 2020 2020 2020 2020 2020 2020 4865 He\n-00022630: 6c6c 6f20 776f 726c 642e 2020 2020 2020 llo world. \n-00022640: 2020 2028 6c69 6e65 2020 3236 290a 2a20 (line 26).* \n-00022650: 7061 7261 6c6c 656c 2070 726f 6a65 6374 parallel project\n-00022660: 696f 6e20 3c31 3e3a 2020 2020 2020 2020 ion <1>: \n-00022670: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-00022680: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-00022690: 6520 2031 3829 0a2a 2070 6172 616c 6c65 e 18).* paralle\n-000226a0: 6c20 7072 6f6a 6563 7469 6f6e 203c 323e l projection <2>\n-000226b0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000226c0: 5069 6374 7572 6520 626f 782e 2020 2020 Picture box. \n-000226d0: 2020 2020 2028 6c69 6e65 2020 3135 290a (line 15).\n-000226e0: 2a20 7061 7265 6e74 6865 7365 733a 2020 * parentheses: \n+00022310: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00022320: 696e 6520 2032 3229 0a2a 206f 7074 696f ine 22).* optio\n+00022330: 6e73 2c20 7377 6570 7420 6f62 6a65 6374 ns, swept object\n+00022340: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+00022350: 2020 5377 6570 7420 6c69 6e65 732e 2020 Swept lines. \n+00022360: 2020 2020 2020 2028 6c69 6e65 2020 3236 (line 26\n+00022370: 290a 2a20 6f70 7469 6f6e 732c 2073 7765 ).* options, swe\n+00022380: 7074 206f 626a 6563 7420 3c33 3e3a 2020 pt object <3>: \n+00022390: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+000223a0: 206c 696e 6573 2e20 2020 2020 2020 2020 lines. \n+000223b0: 286c 696e 6520 2034 3829 0a2a 206f 7264 (line 48).* ord\n+000223c0: 6572 2c20 706f 6c79 676f 6e20 7665 7274 er, polygon vert\n+000223d0: 6578 3a20 2020 2020 2020 2020 2020 2020 ex: \n+000223e0: 2020 2020 4865 6c6c 6f20 776f 726c 642e Hello world.\n+000223f0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00022400: 3339 290a 2a20 6f72 6465 722c 2070 6f6c 39).* order, pol\n+00022410: 7967 6f6e 2076 6572 7465 7820 3c31 3e3a ygon vertex <1>:\n+00022420: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00022430: 7074 206c 696e 6573 2e20 2020 2020 2020 pt lines. \n+00022440: 2020 286c 696e 6520 2031 3429 0a2a 206f (line 14).* o\n+00022450: 7264 6572 2c20 706f 6c79 676f 6e20 7665 rder, polygon ve\n+00022460: 7274 6578 203c 323e 3a20 2020 2020 2020 rtex <2>: \n+00022470: 2020 2020 2020 5377 6570 7420 6c69 6e65 Swept line\n+00022480: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n+00022490: 2020 3430 290a 2a20 6f72 6465 722c 2070 40).* order, p\n+000224a0: 6f6c 7967 6f6e 2076 6572 7465 7820 3c33 olygon vertex <3\n+000224b0: 3e3a 2020 2020 2020 2020 2020 2020 2053 >: S\n+000224c0: 7765 7074 2070 6f6c 7967 6f6e 732e 2020 wept polygons. \n+000224d0: 2020 2020 286c 696e 6520 2031 3929 0a2a (line 19).*\n+000224e0: 206f 7264 6572 2c20 706f 6c79 676f 6e20 order, polygon \n+000224f0: 7665 7274 6578 203c 343e 3a20 2020 2020 vertex <4>: \n+00022500: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n+00022510: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n+00022520: 6e65 2020 3337 290a 2a20 6f72 6465 722c ne 37).* order,\n+00022530: 2070 6f6c 7967 6f6e 2076 6572 7465 7820 polygon vertex \n+00022540: 3c35 3e3a 2020 2020 2020 2020 2020 2020 <5>: \n+00022550: 204f 7665 7276 6965 772e 2020 2020 2020 Overview. \n+00022560: 2020 2020 2020 286c 696e 6520 2035 3529 (line 55)\n+00022570: 0a2a 206f 7574 7075 7420 6c61 6e67 7561 .* output langua\n+00022580: 6765 3a20 2020 2020 2020 2020 2020 2020 ge: \n+00022590: 2020 2020 2020 2020 2020 4c61 6e67 7561 Langua\n+000225a0: 6765 2e20 2020 2020 2020 2020 2020 2028 ge. (\n+000225b0: 6c69 6e65 2020 2036 290a 2a20 6f75 7473 line 6).* outs\n+000225c0: 6964 6520 6f66 2061 2070 6f6c 7967 6f6e ide of a polygon\n+000225d0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+000225e0: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20 Hello world. \n+000225f0: 2020 2020 2020 2020 286c 696e 6520 2033 (line 3\n+00022600: 3729 0a2a 2070 6172 616c 6c65 6c20 7072 7).* parallel pr\n+00022610: 6f6a 6563 7469 6f6e 3a20 2020 2020 2020 ojection: \n+00022620: 2020 2020 2020 2020 2020 2020 4865 6c6c Hell\n+00022630: 6f20 776f 726c 642e 2020 2020 2020 2020 o world. \n+00022640: 2028 6c69 6e65 2020 3236 290a 2a20 7061 (line 26).* pa\n+00022650: 7261 6c6c 656c 2070 726f 6a65 6374 696f rallel projectio\n+00022660: 6e20 3c31 3e3a 2020 2020 2020 2020 2020 n <1>: \n+00022670: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+00022680: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+00022690: 2031 3829 0a2a 2070 6172 616c 6c65 6c20 18).* parallel \n+000226a0: 7072 6f6a 6563 7469 6f6e 203c 323e 3a20 projection <2>: \n+000226b0: 2020 2020 2020 2020 2020 2020 2020 5069 Pi\n+000226c0: 6374 7572 6520 626f 782e 2020 2020 2020 cture box. \n+000226d0: 2020 2028 6c69 6e65 2020 3135 290a 2a20 (line 15).* \n+000226e0: 7061 7265 6e74 6865 7365 733a 2020 2020 parentheses: \n 000226f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022700: 2020 2020 2020 2020 2054 776f 2d6f 7065 Two-ope\n-00022710: 7261 6e64 2028 6269 6e61 7279 2920 666f rand (binary) fo\n-00022720: 726d 732e 0a20 2020 2020 2020 2020 2020 rms.. \n+00022700: 2020 2020 2020 2054 776f 2d6f 7065 7261 Two-opera\n+00022710: 6e64 2028 6269 6e61 7279 2920 666f 726d nd (binary) form\n+00022720: 732e 0a20 2020 2020 2020 2020 2020 2020 s.. \n 00022730: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022740: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022750: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022760: 2020 2028 6c69 6e65 2020 3538 290a 2a20 (line 58).* \n-00022770: 7065 7273 7065 6374 6976 6520 7072 6f6a perspective proj\n-00022780: 6563 7469 6f6e 3a20 2020 2020 2020 2020 ection: \n-00022790: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-000227a0: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-000227b0: 6520 2031 3929 0a2a 2070 6572 7370 6563 e 19).* perspec\n-000227c0: 7469 7665 2070 726f 6a65 6374 696f 6e20 tive projection \n-000227d0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-000227e0: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-000227f0: 6c73 2e20 2028 6c69 6e65 2020 3231 290a ls. (line 21).\n-00022800: 2a20 7065 7273 7065 6374 6976 6520 7072 * perspective pr\n-00022810: 6f6a 6563 7469 6f6e 203c 323e 3a20 2020 ojection <2>: \n-00022820: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n-00022830: 772e 2020 2020 2020 2020 2020 2020 286c w. (l\n-00022840: 696e 6520 2020 3729 0a2a 2070 6963 7475 ine 7).* pictu\n-00022850: 7265 2062 6f78 3a20 2020 2020 2020 2020 re box: \n+00022760: 2028 6c69 6e65 2020 3538 290a 2a20 7065 (line 58).* pe\n+00022770: 7273 7065 6374 6976 6520 7072 6f6a 6563 rspective projec\n+00022780: 7469 6f6e 3a20 2020 2020 2020 2020 2020 tion: \n+00022790: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+000227a0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+000227b0: 2031 3929 0a2a 2070 6572 7370 6563 7469 19).* perspecti\n+000227c0: 7665 2070 726f 6a65 6374 696f 6e20 3c31 ve projection <1\n+000227d0: 3e3a 2020 2020 2020 2020 2020 2020 5472 >: Tr\n+000227e0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+000227f0: 2e20 2028 6c69 6e65 2020 3231 290a 2a20 . (line 21).* \n+00022800: 7065 7273 7065 6374 6976 6520 7072 6f6a perspective proj\n+00022810: 6563 7469 6f6e 203c 323e 3a20 2020 2020 ection <2>: \n+00022820: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n+00022830: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00022840: 6520 2020 3729 0a2a 2070 6963 7475 7265 e 7).* picture\n+00022850: 2062 6f78 3a20 2020 2020 2020 2020 2020 box: \n 00022860: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022870: 2020 5069 6374 7572 6520 626f 782e 2020 Picture box. \n-00022880: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n-00022890: 290a 2a20 706c 616e 6172 6974 7920 6f66 ).* planarity of\n-000228a0: 2070 6f6c 7967 6f6e 733a 2020 2020 2020 polygons: \n-000228b0: 2020 2020 2020 2020 2020 2050 6f6c 7967 Polyg\n-000228c0: 6f6e 732e 2020 2020 2020 2020 2020 2020 ons. \n-000228d0: 286c 696e 6520 2031 3029 0a2a 2070 6c61 (line 10).* pla\n-000228e0: 6e61 7269 7479 206f 6620 706f 6c79 676f narity of polygo\n-000228f0: 6e73 203c 313e 3a20 2020 2020 2020 2020 ns <1>: \n-00022900: 2020 2020 5377 6565 7020 6661 6365 2073 Sweep face s\n-00022910: 706c 6974 7469 6e67 2e0a 2020 2020 2020 plitting.. \n+00022870: 5069 6374 7572 6520 626f 782e 2020 2020 Picture box. \n+00022880: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+00022890: 2a20 706c 616e 6172 6974 7920 6f66 2070 * planarity of p\n+000228a0: 6f6c 7967 6f6e 733a 2020 2020 2020 2020 olygons: \n+000228b0: 2020 2020 2020 2020 2050 6f6c 7967 6f6e Polygon\n+000228c0: 732e 2020 2020 2020 2020 2020 2020 286c s. (l\n+000228d0: 696e 6520 2031 3029 0a2a 2070 6c61 6e61 ine 10).* plana\n+000228e0: 7269 7479 206f 6620 706f 6c79 676f 6e73 rity of polygons\n+000228f0: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00022900: 2020 5377 6565 7020 6661 6365 2073 706c Sweep face spl\n+00022910: 6974 7469 6e67 2e0a 2020 2020 2020 2020 itting.. \n 00022920: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022930: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022940: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022950: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n-00022960: 3729 0a2a 2070 6f69 6e74 2064 6566 696e 7).* point defin\n-00022970: 6974 696f 6e3a 2020 2020 2020 2020 2020 ition: \n-00022980: 2020 2020 2020 2020 2020 2020 4472 6177 Draw\n-00022990: 696e 6720 6120 736f 6c69 642e 2020 2020 ing a solid. \n-000229a0: 2028 6c69 6e65 2020 3233 290a 2a20 706f (line 23).* po\n-000229b0: 696e 7420 6c69 7374 3a20 2020 2020 2020 int list: \n+00022950: 2020 2020 2020 286c 696e 6520 2020 3729 (line 7)\n+00022960: 0a2a 2070 6f69 6e74 2064 6566 696e 6974 .* point definit\n+00022970: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n+00022980: 2020 2020 2020 2020 2020 4472 6177 696e Drawin\n+00022990: 6720 6120 736f 6c69 642e 2020 2020 2028 g a solid. (\n+000229a0: 6c69 6e65 2020 3233 290a 2a20 706f 696e line 23).* poin\n+000229b0: 7420 6c69 7374 3a20 2020 2020 2020 2020 t list: \n 000229c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000229d0: 2020 2020 2053 7765 7074 2070 6f69 6e74 Swept point\n-000229e0: 732e 2020 2020 2020 2020 286c 696e 6520 s. (line \n-000229f0: 2020 3929 0a2a 2070 6f69 6e74 206c 6974 9).* point lit\n-00022a00: 6572 616c 3a20 2020 2020 2020 2020 2020 eral: \n-00022a10: 2020 2020 2020 2020 2020 2020 2020 506f Po\n-00022a20: 696e 7420 616e 6420 7665 6374 6f72 206c int and vector l\n-00022a30: 6974 6572 616c 732e 0a20 2020 2020 2020 iterals.. \n+000229d0: 2020 2053 7765 7074 2070 6f69 6e74 732e Swept points.\n+000229e0: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+000229f0: 3929 0a2a 2070 6f69 6e74 206c 6974 6572 9).* point liter\n+00022a00: 616c 3a20 2020 2020 2020 2020 2020 2020 al: \n+00022a10: 2020 2020 2020 2020 2020 2020 506f 696e Poin\n+00022a20: 7420 616e 6420 7665 6374 6f72 206c 6974 t and vector lit\n+00022a30: 6572 616c 732e 0a20 2020 2020 2020 2020 erals.. \n 00022a40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022a50: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022a60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022a70: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n-00022a80: 290a 2a20 706f 696e 7420 7265 6665 7265 ).* point refere\n-00022a90: 6e63 653a 2020 2020 2020 2020 2020 2020 nce: \n-00022aa0: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n-00022ab0: 206f 6620 7265 6665 7265 6e63 6573 2e20 of references. \n-00022ac0: 286c 696e 6520 2031 3429 0a2a 2070 6f69 (line 14).* poi\n-00022ad0: 6e74 2073 7765 6570 3a20 2020 2020 2020 nt sweep: \n+00022a70: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+00022a80: 2a20 706f 696e 7420 7265 6665 7265 6e63 * point referenc\n+00022a90: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n+00022aa0: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n+00022ab0: 6620 7265 6665 7265 6e63 6573 2e20 286c f references. (l\n+00022ac0: 696e 6520 2031 3429 0a2a 2070 6f69 6e74 ine 14).* point\n+00022ad0: 2073 7765 6570 3a20 2020 2020 2020 2020 sweep: \n 00022ae0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022af0: 2020 2020 5377 6570 7420 6f62 6a65 6374 Swept object\n-00022b00: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. (line \n-00022b10: 3131 290a 2a20 706f 696e 7420 7377 6565 11).* point swee\n-00022b20: 7020 3c31 3e3a 2020 2020 2020 2020 2020 p <1>: \n-00022b30: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-00022b40: 7074 2070 6f69 6e74 732e 2020 2020 2020 pt points. \n-00022b50: 2020 286c 696e 6520 2020 3629 0a2a 2070 (line 6).* p\n-00022b60: 6f6c 7967 6f6e 2073 7765 6570 3a20 2020 olygon sweep: \n+00022af0: 2020 5377 6570 7420 6f62 6a65 6374 732e Swept objects.\n+00022b00: 2020 2020 2020 2028 6c69 6e65 2020 3131 (line 11\n+00022b10: 290a 2a20 706f 696e 7420 7377 6565 7020 ).* point sweep \n+00022b20: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n+00022b30: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n+00022b40: 2070 6f69 6e74 732e 2020 2020 2020 2020 points. \n+00022b50: 286c 696e 6520 2020 3629 0a2a 2070 6f6c (line 6).* pol\n+00022b60: 7967 6f6e 2073 7765 6570 3a20 2020 2020 ygon sweep: \n 00022b70: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022b80: 2020 2020 2020 506f 6c79 676f 6e20 7377 Polygon sw\n-00022b90: 6565 7073 2e20 2020 2020 2028 6c69 6e65 eeps. (line\n-00022ba0: 2020 2036 290a 2a20 706f 6c79 676f 6e20 6).* polygon \n-00022bb0: 7377 6565 7020 3c31 3e3a 2020 2020 2020 sweep <1>: \n-00022bc0: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-00022bd0: 7765 7074 2070 6f6c 7967 6f6e 732e 2020 wept polygons. \n-00022be0: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n-00022bf0: 2070 6f6c 7967 6f6e 2073 7765 6570 203c polygon sweep <\n-00022c00: 323e 3a20 2020 2020 2020 2020 2020 2020 2>: \n-00022c10: 2020 2020 2020 2020 4120 6869 6572 6172 A hierar\n-00022c20: 6368 6963 616c 206d 6f64 656c 2e0a 2020 chical model.. \n+00022b80: 2020 2020 506f 6c79 676f 6e20 7377 6565 Polygon swee\n+00022b90: 7073 2e20 2020 2020 2028 6c69 6e65 2020 ps. (line \n+00022ba0: 2036 290a 2a20 706f 6c79 676f 6e20 7377 6).* polygon sw\n+00022bb0: 6565 7020 3c31 3e3a 2020 2020 2020 2020 eep <1>: \n+00022bc0: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00022bd0: 7074 2070 6f6c 7967 6f6e 732e 2020 2020 pt polygons. \n+00022be0: 2020 286c 696e 6520 2020 3629 0a2a 2070 (line 6).* p\n+00022bf0: 6f6c 7967 6f6e 2073 7765 6570 203c 323e olygon sweep <2>\n+00022c00: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00022c10: 2020 2020 2020 4120 6869 6572 6172 6368 A hierarch\n+00022c20: 6963 616c 206d 6f64 656c 2e0a 2020 2020 ical model.. \n 00022c30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022c40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00022c50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022c60: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n-00022c70: 6520 3132 3229 0a2a 2070 6f6c 7967 6f6e e 122).* polygon\n-00022c80: 2076 6572 7465 7820 6f72 6465 723a 2020 vertex order: \n-00022c90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022ca0: 4865 6c6c 6f20 776f 726c 642e 2020 2020 Hello world. \n-00022cb0: 2020 2020 2028 6c69 6e65 2020 3339 290a (line 39).\n-00022cc0: 2a20 706f 6c79 676f 6e20 7665 7274 6578 * polygon vertex\n-00022cd0: 206f 7264 6572 203c 313e 3a20 2020 2020 order <1>: \n-00022ce0: 2020 2020 2020 2020 2053 7765 7074 206c Swept l\n-00022cf0: 696e 6573 2e20 2020 2020 2020 2020 286c ines. (l\n-00022d00: 696e 6520 2031 3429 0a2a 2070 6f6c 7967 ine 14).* polyg\n-00022d10: 6f6e 2076 6572 7465 7820 6f72 6465 7220 on vertex order \n-00022d20: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n-00022d30: 2020 5377 6570 7420 6c69 6e65 732e 2020 Swept lines. \n-00022d40: 2020 2020 2020 2028 6c69 6e65 2020 3430 (line 40\n-00022d50: 290a 2a20 706f 6c79 676f 6e20 7665 7274 ).* polygon vert\n-00022d60: 6578 206f 7264 6572 203c 333e 3a20 2020 ex order <3>: \n-00022d70: 2020 2020 2020 2020 2020 2053 7765 7074 Swept\n-00022d80: 2070 6f6c 7967 6f6e 732e 2020 2020 2020 polygons. \n-00022d90: 286c 696e 6520 2031 3929 0a2a 2070 6f6c (line 19).* pol\n-00022da0: 7967 6f6e 2076 6572 7465 7820 6f72 6465 ygon vertex orde\n-00022db0: 7220 3c34 3e3a 2020 2020 2020 2020 2020 r <4>: \n-00022dc0: 2020 2020 4f76 6572 7669 6577 2e20 2020 Overview. \n-00022dd0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00022de0: 3337 290a 2a20 706f 6c79 676f 6e20 7665 37).* polygon ve\n-00022df0: 7274 6578 206f 7264 6572 203c 353e 3a20 rtex order <5>: \n-00022e00: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n-00022e10: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n-00022e20: 2020 286c 696e 6520 2035 3529 0a2a 2070 (line 55).* p\n-00022e30: 6f6c 7967 6f6e 2c20 626f 6479 3a20 2020 olygon, body: \n+00022c60: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n+00022c70: 3132 3229 0a2a 2070 6f6c 7967 6f6e 2076 122).* polygon v\n+00022c80: 6572 7465 7820 6f72 6465 723a 2020 2020 ertex order: \n+00022c90: 2020 2020 2020 2020 2020 2020 2020 4865 He\n+00022ca0: 6c6c 6f20 776f 726c 642e 2020 2020 2020 llo world. \n+00022cb0: 2020 2028 6c69 6e65 2020 3339 290a 2a20 (line 39).* \n+00022cc0: 706f 6c79 676f 6e20 7665 7274 6578 206f polygon vertex o\n+00022cd0: 7264 6572 203c 313e 3a20 2020 2020 2020 rder <1>: \n+00022ce0: 2020 2020 2020 2053 7765 7074 206c 696e Swept lin\n+00022cf0: 6573 2e20 2020 2020 2020 2020 286c 696e es. (lin\n+00022d00: 6520 2031 3429 0a2a 2070 6f6c 7967 6f6e e 14).* polygon\n+00022d10: 2076 6572 7465 7820 6f72 6465 7220 3c32 vertex order <2\n+00022d20: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00022d30: 5377 6570 7420 6c69 6e65 732e 2020 2020 Swept lines. \n+00022d40: 2020 2020 2028 6c69 6e65 2020 3430 290a (line 40).\n+00022d50: 2a20 706f 6c79 676f 6e20 7665 7274 6578 * polygon vertex\n+00022d60: 206f 7264 6572 203c 333e 3a20 2020 2020 order <3>: \n+00022d70: 2020 2020 2020 2020 2053 7765 7074 2070 Swept p\n+00022d80: 6f6c 7967 6f6e 732e 2020 2020 2020 286c olygons. 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(line\n+00022f00: 2020 2039 290a 2a20 706f 6c79 676f 6e2c 9).* polygon,\n+00022f10: 2065 6e64 3a20 2020 2020 2020 2020 2020 end: \n+00022f20: 2020 2020 2020 2020 2020 2020 2020 2053 S\n+00022f30: 7765 7074 206c 696e 6573 2e20 2020 2020 wept lines. \n+00022f40: 2020 2020 286c 696e 6520 2033 3829 0a2a (line 38).*\n+00022f50: 2070 6f6c 7967 6f6e 2c20 656e 6420 3c31 polygon, end <1\n+00022f60: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00022f70: 2020 2020 2020 2020 5377 6570 7420 706f Swept po\n+00022f80: 6c79 676f 6e73 2e20 2020 2020 2028 6c69 lygons. (li\n+00022f90: 6e65 2020 3135 290a 2a20 706f 6c79 676f ne 15).* polygo\n+00022fa0: 6e2c 206f 7574 7369 6465 206f 663a 2020 n, outside of: \n 00022fb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00022fc0: 2020 2048 656c 6c6f 2077 6f72 6c64 2e20 Hello world. \n-00022fd0: 2020 2020 2020 2020 286c 696e 6520 2033 (line 3\n-00022fe0: 3729 0a2a 2070 6f6c 7967 6f6e 2c20 706c 7).* polygon, pl\n-00022ff0: 616e 6172 3a20 2020 2020 2020 2020 2020 anar: \n-00023000: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-00023010: 676f 6e73 2e20 2020 2020 2020 2020 2020 gons. \n-00023020: 2028 6c69 6e65 2020 3130 290a 2a20 706f (line 10).* po\n-00023030: 6c79 676f 6e2c 2070 6c61 6e61 7220 3c31 lygon, planar <1\n-00023040: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n-00023050: 2020 2020 2053 7765 6570 2066 6163 6520 Sweep face \n-00023060: 7370 6c69 7474 696e 672e 0a20 2020 2020 splitting.. \n+00022fc0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n+00022fd0: 2020 2020 2020 286c 696e 6520 2033 3729 (line 37)\n+00022fe0: 0a2a 2070 6f6c 7967 6f6e 2c20 706c 616e .* polygon, plan\n+00022ff0: 6172 3a20 2020 2020 2020 2020 2020 2020 ar: \n+00023000: 2020 2020 2020 2020 2020 506f 6c79 676f Polygo\n+00023010: 6e73 2e20 2020 2020 2020 2020 2020 2028 ns. (\n+00023020: 6c69 6e65 2020 3130 290a 2a20 706f 6c79 line 10).* poly\n+00023030: 676f 6e2c 2070 6c61 6e61 7220 3c31 3e3a gon, planar <1>:\n+00023040: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00023050: 2020 2053 7765 6570 2066 6163 6520 7370 Sweep face sp\n+00023060: 6c69 7474 696e 672e 0a20 2020 2020 2020 litting.. \n 00023070: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023080: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023090: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000230a0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-000230b0: 2037 290a 2a20 7072 6563 6564 656e 6365 7).* precedence\n-000230c0: 2c20 6f70 6572 6174 6f72 3a20 2020 2020 , operator: \n-000230d0: 2020 2020 2020 2020 2020 2020 2054 776f Two\n-000230e0: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n-000230f0: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n+000230a0: 2020 2020 2020 2028 6c69 6e65 2020 2037 (line 7\n+000230b0: 290a 2a20 7072 6563 6564 656e 6365 2c20 ).* precedence, \n+000230c0: 6f70 6572 6174 6f72 3a20 2020 2020 2020 operator: \n+000230d0: 2020 2020 2020 2020 2020 2054 776f 2d6f Two-o\n+000230e0: 7065 7261 6e64 2028 6269 6e61 7279 2920 perand (binary) \n+000230f0: 666f 726d 732e 0a20 2020 2020 2020 2020 forms.. \n 00023100: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023110: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023120: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023130: 2020 2020 2020 2028 6c69 6e65 2020 3435 (line 45\n-00023140: 290a 2a20 7072 6f67 7261 6d2c 2068 656c ).* program, hel\n-00023150: 6c6f 2077 6f72 6c64 3a20 2020 2020 2020 lo world: \n-00023160: 2020 2020 2020 2020 2020 2048 656c 6c6f Hello\n-00023170: 2077 6f72 6c64 2e20 2020 2020 2020 2020 world. \n-00023180: 286c 696e 6520 2020 3729 0a2a 2070 726f (line 7).* pro\n-00023190: 6a65 6374 696f 6e2c 2070 6172 616c 6c65 jection, paralle\n-000231a0: 6c3a 2020 2020 2020 2020 2020 2020 2020 l: \n-000231b0: 2020 2020 4865 6c6c 6f20 776f 726c 642e Hello world.\n-000231c0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-000231d0: 3236 290a 2a20 7072 6f6a 6563 7469 6f6e 26).* projection\n-000231e0: 2c20 7061 7261 6c6c 656c 203c 313e 3a20 , parallel <1>: \n-000231f0: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n-00023200: 6e73 666f 726d 206c 6974 6572 616c 732e nsform literals.\n-00023210: 2020 286c 696e 6520 2031 3829 0a2a 2070 (line 18).* p\n-00023220: 726f 6a65 6374 696f 6e2c 2070 6172 616c rojection, paral\n-00023230: 6c65 6c20 3c32 3e3a 2020 2020 2020 2020 lel <2>: \n-00023240: 2020 2020 2020 5069 6374 7572 6520 626f Picture bo\n-00023250: 782e 2020 2020 2020 2020 2028 6c69 6e65 x. 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(li\n-000232f0: 6e65 2020 3231 290a 2a20 7072 6f6a 6563 ne 21).* projec\n-00023300: 7469 6f6e 2c20 7065 7273 7065 6374 6976 tion, perspectiv\n-00023310: 6520 3c32 3e3a 2020 2020 2020 2020 2020 e <2>: \n-00023320: 204f 7665 7276 6965 772e 2020 2020 2020 Overview. \n-00023330: 2020 2020 2020 286c 696e 6520 2020 3729 (line 7)\n-00023340: 0a2a 2070 7365 7564 6f2d 6f70 7469 6f6e .* pseudo-option\n-00023350: 733a 2020 2020 2020 2020 2020 2020 2020 s: \n-00023360: 2020 2020 2020 2020 2020 5469 6b5a 2f50 TikZ/P\n-00023370: 4746 2075 7365 722d 6465 6669 6e65 6420 GF user-defined \n-00023380: 7374 796c 6573 2e0a 2020 2020 2020 2020 styles.. \n+00023130: 2020 2020 2028 6c69 6e65 2020 3435 290a (line 45).\n+00023140: 2a20 7072 6f67 7261 6d2c 2068 656c 6c6f * program, hello\n+00023150: 2077 6f72 6c64 3a20 2020 2020 2020 2020 world: \n+00023160: 2020 2020 2020 2020 2048 656c 6c6f 2077 Hello w\n+00023170: 6f72 6c64 2e20 2020 2020 2020 2020 286c orld. 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(line\n+000232f0: 2020 3231 290a 2a20 7072 6f6a 6563 7469 21).* projecti\n+00023300: 6f6e 2c20 7065 7273 7065 6374 6976 6520 on, perspective \n+00023310: 3c32 3e3a 2020 2020 2020 2020 2020 204f <2>: O\n+00023320: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n+00023330: 2020 2020 286c 696e 6520 2020 3729 0a2a (line 7).*\n+00023340: 2070 7365 7564 6f2d 6f70 7469 6f6e 733a pseudo-options:\n+00023350: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00023360: 2020 2020 2020 2020 5469 6b5a 2f50 4746 TikZ/PGF\n+00023370: 2075 7365 722d 6465 6669 6e65 6420 7374 user-defined st\n+00023380: 796c 6573 2e0a 2020 2020 2020 2020 2020 yles.. \n 00023390: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000233a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000233b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000233c0: 2020 2020 2020 286c 696e 6520 2032 3529 (line 25)\n-000233d0: 0a2a 2070 7366 7261 6d65 626f 783a 2020 .* psframebox: \n+000233c0: 2020 2020 286c 696e 6520 2032 3529 0a2a (line 25).*\n+000233d0: 2070 7366 7261 6d65 626f 783a 2020 2020 psframebox: \n 000233e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000233f0: 2020 2020 2020 2020 2020 4672 616d 652e Frame.\n-00023400: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-00023410: 6c69 6e65 2020 2038 290a 2a20 7073 7069 line 8).* pspi\n-00023420: 6374 7572 653a 2020 2020 2020 2020 2020 cture: \n+000233f0: 2020 2020 2020 2020 4672 616d 652e 2020 Frame. \n+00023400: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+00023410: 6e65 2020 2038 290a 2a20 7073 7069 6374 ne 8).* pspict\n+00023420: 7572 653a 2020 2020 2020 2020 2020 2020 ure: \n 00023430: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023440: 2020 2050 6963 7475 7265 2062 6f78 2e20 Picture box. \n-00023450: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n-00023460: 3029 0a2a 2050 5354 7269 636b 733a 2020 0).* PSTricks: \n+00023440: 2050 6963 7475 7265 2062 6f78 2e20 2020 Picture box. \n+00023450: 2020 2020 2020 286c 696e 6520 2031 3029 (line 10)\n+00023460: 0a2a 2050 5354 7269 636b 733a 2020 2020 .* PSTricks: \n 00023470: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023480: 2020 2020 2020 2020 2020 2020 4162 6f75 Abou\n-00023490: 7420 736b 6574 6368 2e20 2020 2020 2020 t sketch. \n-000234a0: 2028 6c69 6e65 2020 3231 290a 2a20 7175 (line 21).* qu\n-000234b0: 6f74 696e 672c 2073 7065 6369 616c 3a20 oting, special: \n+00023480: 2020 2020 2020 2020 2020 4162 6f75 7420 About \n+00023490: 736b 6574 6368 2e20 2020 2020 2020 2028 sketch. (\n+000234a0: 6c69 6e65 2020 3231 290a 2a20 7175 6f74 line 21).* quot\n+000234b0: 696e 672c 2073 7065 6369 616c 3a20 2020 ing, special: \n 000234c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000234d0: 2020 2020 2053 7065 6369 616c 206f 626a Special obj\n-000234e0: 6563 7473 2e20 2020 2020 286c 696e 6520 ects. (line \n-000234f0: 2032 3029 0a2a 2071 756f 7469 6e67 2c20 20).* quoting, \n-00023500: 7370 6563 6961 6c20 3c31 3e3a 2020 2020 special <1>: \n-00023510: 2020 2020 2020 2020 2020 2020 2020 5370 Sp\n-00023520: 6563 6961 6c73 2e20 2020 2020 2020 2020 ecials. \n-00023530: 2020 2028 6c69 6e65 2020 2038 290a 2a20 (line 8).* \n-00023540: 7265 6665 7265 6e63 652c 2064 7261 7761 reference, drawa\n-00023550: 626c 653a 2020 2020 2020 2020 2020 2020 ble: \n-00023560: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n-00023570: 616e 7366 6f72 6d73 2e20 2020 286c 696e ansforms. 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(l\n-00023610: 696e 6520 2034 3729 0a2a 2072 6566 6572 ine 47).* refer\n-00023620: 656e 6365 2c20 6472 6177 6162 6c65 203c ence, drawable <\n-00023630: 333e 3a20 2020 2020 2020 2020 2020 2020 3>: \n-00023640: 2020 4f76 6572 7669 6577 2e20 2020 2020 Overview. \n-00023650: 2020 2020 2020 2028 6c69 6e65 2020 3537 (line 57\n-00023660: 290a 2a20 7265 6665 7265 6e63 652c 206d ).* reference, m\n-00023670: 756c 7469 706c 6520 6f70 7469 6f6e 733a ultiple options:\n-00023680: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n-00023690: 206f 6620 7265 6665 7265 6e63 6573 2e20 of references. \n-000236a0: 286c 696e 6520 2031 3829 0a2a 2072 6566 (line 18).* ref\n-000236b0: 6572 656e 6365 2c20 6f70 7469 6f6e 733a erence, options:\n+000234d0: 2020 2053 7065 6369 616c 206f 626a 6563 Special objec\n+000234e0: 7473 2e20 2020 2020 286c 696e 6520 2032 ts. (line 2\n+000234f0: 3029 0a2a 2071 756f 7469 6e67 2c20 7370 0).* quoting, sp\n+00023500: 6563 6961 6c20 3c31 3e3a 2020 2020 2020 ecial <1>: \n+00023510: 2020 2020 2020 2020 2020 2020 5370 6563 Spec\n+00023520: 6961 6c73 2e20 2020 2020 2020 2020 2020 ials. \n+00023530: 2028 6c69 6e65 2020 2038 290a 2a20 7265 (line 8).* re\n+00023540: 6665 7265 6e63 652c 2064 7261 7761 626c ference, drawabl\n+00023550: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n+00023560: 2020 2020 204f 626a 6563 7420 7472 616e Object tran\n+00023570: 7366 6f72 6d73 2e20 2020 286c 696e 6520 sforms. (line \n+00023580: 2033 3329 0a2a 2072 6566 6572 656e 6365 33).* reference\n+00023590: 2c20 6472 6177 6162 6c65 203c 313e 3a20 , drawable <1>: \n+000235a0: 2020 2020 2020 2020 2020 2020 2020 466f Fo\n+000235b0: 726d 7320 6f66 2072 6566 6572 656e 6365 rms of reference\n+000235c0: 732e 2028 6c69 6e65 2020 3137 290a 2a20 s. (line 17).* \n+000235d0: 7265 6665 7265 6e63 652c 2064 7261 7761 reference, drawa\n+000235e0: 626c 6520 3c32 3e3a 2020 2020 2020 2020 ble <2>: \n+000235f0: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n+00023600: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+00023610: 6520 2034 3729 0a2a 2072 6566 6572 656e e 47).* referen\n+00023620: 6365 2c20 6472 6177 6162 6c65 203c 333e ce, drawable <3>\n+00023630: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00023640: 4f76 6572 7669 6577 2e20 2020 2020 2020 Overview. \n+00023650: 2020 2020 2028 6c69 6e65 2020 3537 290a (line 57).\n+00023660: 2a20 7265 6665 7265 6e63 652c 206d 756c * reference, mul\n+00023670: 7469 706c 6520 6f70 7469 6f6e 733a 2020 tiple options: \n+00023680: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n+00023690: 6620 7265 6665 7265 6e63 6573 2e20 286c f references. (l\n+000236a0: 696e 6520 2031 3829 0a2a 2072 6566 6572 ine 18).* refer\n+000236b0: 656e 6365 2c20 6f70 7469 6f6e 733a 2020 ence, options: \n 000236c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000236d0: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n-000236e0: 6570 7320 7769 7468 2063 6c6f 7375 7265 eps with closure\n-000236f0: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+000236d0: 2020 506f 6c79 6c69 6e65 2073 7765 6570 Polyline sweep\n+000236e0: 7320 7769 7468 2063 6c6f 7375 7265 2e0a s with closure..\n+000236f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023700: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023710: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023720: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023730: 286c 696e 6520 2032 3429 0a2a 2072 6566 (line 24).* ref\n-00023740: 6572 656e 6365 2c20 6f70 7469 6f6e 7320 erence, options \n-00023750: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00023760: 2020 2020 466f 726d 7320 6f66 2072 6566 Forms of ref\n-00023770: 6572 656e 6365 732e 2028 6c69 6e65 2020 erences. (line \n-00023780: 3138 290a 2a20 7265 6665 7265 6e63 652c 18).* reference,\n-00023790: 2070 6f69 6e74 3a20 2020 2020 2020 2020 point: \n-000237a0: 2020 2020 2020 2020 2020 2020 2044 7261 Dra\n-000237b0: 7769 6e67 2061 2073 6f6c 6964 2e20 2020 wing a solid. \n-000237c0: 2020 286c 696e 6520 2032 3329 0a2a 2072 (line 23).* r\n-000237d0: 6566 6572 656e 6365 2c20 706f 696e 7420 eference, point \n-000237e0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-000237f0: 2020 2020 2020 466f 726d 7320 6f66 2072 Forms of r\n-00023800: 6566 6572 656e 6365 732e 2028 6c69 6e65 eferences. (line\n-00023810: 2020 3134 290a 2a20 7265 6665 7265 6e63 14).* referenc\n-00023820: 652c 2073 6361 6c61 723a 2020 2020 2020 e, scalar: \n-00023830: 2020 2020 2020 2020 2020 2020 2020 2053 S\n-00023840: 7765 7074 206f 626a 6563 7473 2e20 2020 wept objects. \n-00023850: 2020 2020 286c 696e 6520 2031 3329 0a2a (line 13).*\n-00023860: 2072 6566 6572 656e 6365 2c20 7363 616c reference, scal\n-00023870: 6172 203c 313e 3a20 2020 2020 2020 2020 ar <1>: \n-00023880: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n-00023890: 2072 6566 6572 656e 6365 732e 2028 6c69 references. (li\n-000238a0: 6e65 2020 3133 290a 2a20 7265 6665 7265 ne 13).* refere\n-000238b0: 6e63 652c 2074 6167 3a20 2020 2020 2020 nce, tag: \n-000238c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000238d0: 2046 6f72 6d73 206f 6620 6465 6669 6e69 Forms of defini\n-000238e0: 7469 6f6e 732e 0a20 2020 2020 2020 2020 tions.. \n+00023720: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00023730: 696e 6520 2032 3429 0a2a 2072 6566 6572 ine 24).* refer\n+00023740: 656e 6365 2c20 6f70 7469 6f6e 7320 3c31 ence, options <1\n+00023750: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00023760: 2020 466f 726d 7320 6f66 2072 6566 6572 Forms of refer\n+00023770: 656e 6365 732e 2028 6c69 6e65 2020 3138 ences. (line 18\n+00023780: 290a 2a20 7265 6665 7265 6e63 652c 2070 ).* reference, p\n+00023790: 6f69 6e74 3a20 2020 2020 2020 2020 2020 oint: \n+000237a0: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n+000237b0: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n+000237c0: 286c 696e 6520 2032 3329 0a2a 2072 6566 (line 23).* ref\n+000237d0: 6572 656e 6365 2c20 706f 696e 7420 3c31 erence, point <1\n+000237e0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+000237f0: 2020 2020 466f 726d 7320 6f66 2072 6566 Forms of ref\n+00023800: 6572 656e 6365 732e 2028 6c69 6e65 2020 erences. (line \n+00023810: 3134 290a 2a20 7265 6665 7265 6e63 652c 14).* reference,\n+00023820: 2073 6361 6c61 723a 2020 2020 2020 2020 scalar: \n+00023830: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n+00023840: 7074 206f 626a 6563 7473 2e20 2020 2020 pt objects. \n+00023850: 2020 286c 696e 6520 2031 3329 0a2a 2072 (line 13).* r\n+00023860: 6566 6572 656e 6365 2c20 7363 616c 6172 eference, scalar\n+00023870: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n+00023880: 2020 2020 2020 466f 726d 7320 6f66 2072 Forms of r\n+00023890: 6566 6572 656e 6365 732e 2028 6c69 6e65 eferences. (line\n+000238a0: 2020 3133 290a 2a20 7265 6665 7265 6e63 13).* referenc\n+000238b0: 652c 2074 6167 3a20 2020 2020 2020 2020 e, tag: \n+000238c0: 2020 2020 2020 2020 2020 2020 2020 2046 F\n+000238d0: 6f72 6d73 206f 6620 6465 6669 6e69 7469 orms of definiti\n+000238e0: 6f6e 732e 0a20 2020 2020 2020 2020 2020 ons.. \n 000238f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023900: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023910: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023920: 2020 2020 2028 6c69 6e65 2020 3230 290a (line 20).\n-00023930: 2a20 7265 6665 7265 6e63 652c 2074 6167 * reference, tag\n-00023940: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-00023950: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n-00023960: 6620 7265 6665 7265 6e63 6573 2e20 286c f references. (l\n-00023970: 696e 6520 2031 3929 0a2a 2072 6566 6572 ine 19).* refer\n-00023980: 656e 6365 2c20 7472 616e 7366 6f72 6d3a ence, transform:\n+00023920: 2020 2028 6c69 6e65 2020 3230 290a 2a20 (line 20).* \n+00023930: 7265 6665 7265 6e63 652c 2074 6167 203c reference, tag <\n+00023940: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+00023950: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n+00023960: 7265 6665 7265 6e63 6573 2e20 286c 696e references. (lin\n+00023970: 6520 2031 3929 0a2a 2072 6566 6572 656e e 19).* referen\n+00023980: 6365 2c20 7472 616e 7366 6f72 6d3a 2020 ce, transform: \n 00023990: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000239a0: 2020 466f 726d 7320 6f66 2072 6566 6572 Forms of refer\n-000239b0: 656e 6365 732e 2028 6c69 6e65 2020 3136 ences. (line 16\n-000239c0: 290a 2a20 7265 6665 7265 6e63 652c 2074 ).* reference, t\n-000239d0: 7261 6e73 666f 726d 203c 313e 3a20 2020 ransform <1>: \n-000239e0: 2020 2020 2020 2020 2020 204f 7665 7276 Overv\n-000239f0: 6965 772e 2020 2020 2020 2020 2020 2020 iew. \n-00023a00: 286c 696e 6520 2033 3529 0a2a 2072 6566 (line 35).* ref\n-00023a10: 6572 656e 6365 2c20 7665 6374 6f72 3a20 erence, vector: \n+000239a0: 466f 726d 7320 6f66 2072 6566 6572 656e Forms of referen\n+000239b0: 6365 732e 2028 6c69 6e65 2020 3136 290a ces. (line 16).\n+000239c0: 2a20 7265 6665 7265 6e63 652c 2074 7261 * reference, tra\n+000239d0: 6e73 666f 726d 203c 313e 3a20 2020 2020 nsform <1>: \n+000239e0: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n+000239f0: 772e 2020 2020 2020 2020 2020 2020 286c w. (l\n+00023a00: 696e 6520 2033 3529 0a2a 2072 6566 6572 ine 35).* refer\n+00023a10: 656e 6365 2c20 7665 6374 6f72 3a20 2020 ence, vector: \n 00023a20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023a30: 2020 2020 506f 6c79 6c69 6e65 2073 7765 Polyline swe\n-00023a40: 6570 732e 2020 2020 2028 6c69 6e65 2020 eps. (line \n-00023a50: 3230 290a 2a20 7265 6665 7265 6e63 652c 20).* reference,\n-00023a60: 2076 6563 746f 7220 3c31 3e3a 2020 2020 vector <1>: \n-00023a70: 2020 2020 2020 2020 2020 2020 2046 6f72 For\n-00023a80: 6d73 206f 6620 7265 6665 7265 6e63 6573 ms of references\n-00023a90: 2e20 286c 696e 6520 2031 3529 0a2a 2072 . (line 15).* r\n-00023aa0: 6570 6561 7465 6420 6f62 6a65 6374 3a20 epeated object: \n+00023a30: 2020 506f 6c79 6c69 6e65 2073 7765 6570 Polyline sweep\n+00023a40: 732e 2020 2020 2028 6c69 6e65 2020 3230 s. (line 20\n+00023a50: 290a 2a20 7265 6665 7265 6e63 652c 2076 ).* reference, v\n+00023a60: 6563 746f 7220 3c31 3e3a 2020 2020 2020 ector <1>: \n+00023a70: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n+00023a80: 206f 6620 7265 6665 7265 6e63 6573 2e20 of references. \n+00023a90: 286c 696e 6520 2031 3529 0a2a 2072 6570 (line 15).* rep\n+00023aa0: 6561 7465 6420 6f62 6a65 6374 3a20 2020 eated object: \n 00023ab0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023ac0: 2020 2020 2020 5265 7065 6174 732e 2020 Repeats. \n-00023ad0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00023ae0: 2020 2036 290a 2a20 7265 7365 7276 6564 6).* reserved\n-00023af0: 2077 6f72 6473 3a20 2020 2020 2020 2020 words: \n-00023b00: 2020 2020 2020 2020 2020 2020 2020 204b K\n-00023b10: 6579 2061 6e64 2072 6573 6572 7665 6420 ey and reserved \n-00023b20: 776f 7264 732e 0a20 2020 2020 2020 2020 words.. \n+00023ac0: 2020 2020 5265 7065 6174 732e 2020 2020 Repeats. \n+00023ad0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00023ae0: 2036 290a 2a20 7265 7365 7276 6564 2077 6).* reserved w\n+00023af0: 6f72 6473 3a20 2020 2020 2020 2020 2020 ords: \n+00023b00: 2020 2020 2020 2020 2020 2020 204b 6579 Key\n+00023b10: 2061 6e64 2072 6573 6572 7665 6420 776f and reserved wo\n+00023b20: 7264 732e 0a20 2020 2020 2020 2020 2020 rds.. \n 00023b30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023b40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023b50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023b60: 2020 2020 2028 6c69 6e65 2020 3131 290a (line 11).\n-00023b70: 2a20 7269 6768 7420 6861 6e64 2072 756c * right hand rul\n-00023b80: 653a 2020 2020 2020 2020 2020 2020 2020 e: \n-00023b90: 2020 2020 2020 2020 204f 626a 6563 7420 Object \n-00023ba0: 7472 616e 7366 6f72 6d73 2e20 2020 286c transforms. (l\n-00023bb0: 696e 6520 2034 3129 0a2a 2072 6967 6874 ine 41).* right\n-00023bc0: 2d68 616e 6420 636f 6f72 6469 6e61 7465 -hand coordinate\n-00023bd0: 2073 7973 7465 6d3a 2020 2020 2020 2020 system: \n-00023be0: 2020 496e 7472 6f64 7563 7469 6f6e 2062 Introduction b\n-00023bf0: 7920 6578 616d 706c 652e 0a20 2020 2020 y example.. \n+00023b60: 2020 2028 6c69 6e65 2020 3131 290a 2a20 (line 11).* \n+00023b70: 7269 6768 7420 6861 6e64 2072 756c 653a right hand rule:\n+00023b80: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00023b90: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n+00023ba0: 616e 7366 6f72 6d73 2e20 2020 286c 696e ansforms. (lin\n+00023bb0: 6520 2034 3129 0a2a 2072 6967 6874 2d68 e 41).* right-h\n+00023bc0: 616e 6420 636f 6f72 6469 6e61 7465 2073 and coordinate s\n+00023bd0: 7973 7465 6d3a 2020 2020 2020 2020 2020 ystem: \n+00023be0: 496e 7472 6f64 7563 7469 6f6e 2062 7920 Introduction by \n+00023bf0: 6578 616d 706c 652e 0a20 2020 2020 2020 example.. \n 00023c00: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023c10: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023c20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023c30: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00023c40: 3131 290a 2a20 726f 7461 7469 6f6e 3a20 11).* rotation: \n+00023c30: 2020 2020 2020 2028 6c69 6e65 2020 3131 (line 11\n+00023c40: 290a 2a20 726f 7461 7469 6f6e 3a20 2020 ).* rotation: \n 00023c50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023c60: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n-00023c70: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n-00023c80: 2020 286c 696e 6520 2033 3929 0a2a 2072 (line 39).* r\n-00023c90: 6f74 6174 696f 6e20 7472 616e 7366 6f72 otation transfor\n-00023ca0: 6d3a 2020 2020 2020 2020 2020 2020 2020 m: \n-00023cb0: 2020 2020 2020 5472 616e 7366 6f72 6d20 Transform \n-00023cc0: 6c69 7465 7261 6c73 2e20 2028 6c69 6e65 literals. (line\n-00023cd0: 2020 3130 290a 2a20 726f 7461 7469 6f6e 10).* rotation\n-00023ce0: 2074 7261 6e73 666f 726d 203c 313e 3a20 transform <1>: \n-00023cf0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-00023d00: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-00023d10: 6465 6c2e 0a20 2020 2020 2020 2020 2020 del.. \n+00023c60: 2020 2020 2020 2020 2020 204f 626a 6563 Objec\n+00023c70: 7420 7472 616e 7366 6f72 6d73 2e20 2020 t transforms. \n+00023c80: 286c 696e 6520 2033 3929 0a2a 2072 6f74 (line 39).* rot\n+00023c90: 6174 696f 6e20 7472 616e 7366 6f72 6d3a ation transform:\n+00023ca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00023cb0: 2020 2020 5472 616e 7366 6f72 6d20 6c69 Transform li\n+00023cc0: 7465 7261 6c73 2e20 2028 6c69 6e65 2020 terals. (line \n+00023cd0: 3130 290a 2a20 726f 7461 7469 6f6e 2074 10).* rotation t\n+00023ce0: 7261 6e73 666f 726d 203c 313e 3a20 2020 ransform <1>: \n+00023cf0: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+00023d00: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+00023d10: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 00023d20: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023d30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023d40: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023d50: 2020 2028 6c69 6e65 2020 3438 290a 2a20 (line 48).* \n-00023d60: 726f 7461 7469 6f6e 2074 7261 6e73 666f rotation transfo\n-00023d70: 726d 203c 323e 3a20 2020 2020 2020 2020 rm <2>: \n-00023d80: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n-00023d90: 6869 6361 6c20 6d6f 6465 6c2e 0a20 2020 hical model.. \n+00023d50: 2028 6c69 6e65 2020 3438 290a 2a20 726f (line 48).* ro\n+00023d60: 7461 7469 6f6e 2074 7261 6e73 666f 726d tation transform\n+00023d70: 203c 323e 3a20 2020 2020 2020 2020 2020 <2>: \n+00023d80: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n+00023d90: 6361 6c20 6d6f 6465 6c2e 0a20 2020 2020 cal model.. \n 00023da0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023db0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023dc0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023dd0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00023de0: 2020 3538 290a 2a20 726f 7461 7469 6f6e 58).* rotation\n-00023df0: 2074 7261 6e73 666f 726d 203c 333e 3a20 transform <3>: \n-00023e00: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-00023e10: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-00023e20: 6465 6c2e 0a20 2020 2020 2020 2020 2020 del.. \n+00023dd0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00023de0: 3538 290a 2a20 726f 7461 7469 6f6e 2074 58).* rotation t\n+00023df0: 7261 6e73 666f 726d 203c 333e 3a20 2020 ransform <3>: \n+00023e00: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+00023e10: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+00023e20: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 00023e30: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023e40: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023e50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023e60: 2020 2028 6c69 6e65 2020 3738 290a 2a20 (line 78).* \n-00023e70: 726f 7461 7469 6f6e 2074 7261 6e73 666f rotation transfo\n-00023e80: 726d 203c 343e 3a20 2020 2020 2020 2020 rm <4>: \n-00023e90: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n-00023ea0: 6869 6361 6c20 6d6f 6465 6c2e 0a20 2020 hical model.. \n+00023e60: 2028 6c69 6e65 2020 3738 290a 2a20 726f (line 78).* ro\n+00023e70: 7461 7469 6f6e 2074 7261 6e73 666f 726d tation transform\n+00023e80: 203c 343e 3a20 2020 2020 2020 2020 2020 <4>: \n+00023e90: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n+00023ea0: 6361 6c20 6d6f 6465 6c2e 0a20 2020 2020 cal model.. \n 00023eb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023ec0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00023ed0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023ee0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00023ef0: 2020 3933 290a 2a20 726f 7461 7469 6f6e 93).* rotation\n-00023f00: 2c20 6365 6e74 6572 206f 663a 2020 2020 , center of: \n-00023f10: 2020 2020 2020 2020 2020 2020 2020 204f O\n-00023f20: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n-00023f30: 2e20 2020 286c 696e 6520 2020 3829 0a2a . (line 8).*\n-00023f40: 2072 6f74 6174 696f 6e2c 2063 656e 7465 rotation, cente\n-00023f50: 7220 6f66 203c 313e 3a20 2020 2020 2020 r of <1>: \n-00023f60: 2020 2020 2020 2020 4e65 7374 6564 2073 Nested s\n-00023f70: 7765 6570 732e 2020 2020 2020 2028 6c69 weeps. (li\n-00023f80: 6e65 2020 2036 290a 2a20 7275 6e6e 696e ne 6).* runnin\n-00023f90: 6720 736b 6574 6368 3a20 2020 2020 2020 g sketch: \n-00023fa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00023fb0: 2048 656c 6c6f 2077 6f72 6c64 2e20 2020 Hello world. \n-00023fc0: 2020 2020 2020 286c 696e 6520 2020 3929 (line 9)\n-00023fd0: 0a2a 2073 6361 6c61 7220 6465 6669 6e69 .* scalar defini\n-00023fe0: 7469 6f6e 3a20 2020 2020 2020 2020 2020 tion: \n-00023ff0: 2020 2020 2020 2020 2020 5377 6570 7420 Swept \n-00024000: 6f62 6a65 6374 732e 2020 2020 2020 2028 objects. (\n-00024010: 6c69 6e65 2020 3133 290a 2a20 7363 616c line 13).* scal\n-00024020: 6172 206c 6974 6572 616c 3a20 2020 2020 ar literal: \n+00023ee0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00023ef0: 3933 290a 2a20 726f 7461 7469 6f6e 2c20 93).* rotation, \n+00023f00: 6365 6e74 6572 206f 663a 2020 2020 2020 center of: \n+00023f10: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n+00023f20: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n+00023f30: 2020 286c 696e 6520 2020 3829 0a2a 2072 (line 8).* r\n+00023f40: 6f74 6174 696f 6e2c 2063 656e 7465 7220 otation, center \n+00023f50: 6f66 203c 313e 3a20 2020 2020 2020 2020 of <1>: \n+00023f60: 2020 2020 2020 4e65 7374 6564 2073 7765 Nested swe\n+00023f70: 6570 732e 2020 2020 2020 2028 6c69 6e65 eps. (line\n+00023f80: 2020 2036 290a 2a20 7275 6e6e 696e 6720 6).* running \n+00023f90: 736b 6574 6368 3a20 2020 2020 2020 2020 sketch: \n+00023fa0: 2020 2020 2020 2020 2020 2020 2020 2048 H\n+00023fb0: 656c 6c6f 2077 6f72 6c64 2e20 2020 2020 ello world. \n+00023fc0: 2020 2020 286c 696e 6520 2020 3929 0a2a (line 9).*\n+00023fd0: 2073 6361 6c61 7220 6465 6669 6e69 7469 scalar definiti\n+00023fe0: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n+00023ff0: 2020 2020 2020 2020 5377 6570 7420 6f62 Swept ob\n+00024000: 6a65 6374 732e 2020 2020 2020 2028 6c69 jects. (li\n+00024010: 6e65 2020 3133 290a 2a20 7363 616c 6172 ne 13).* scalar\n+00024020: 206c 6974 6572 616c 3a20 2020 2020 2020 literal: \n 00024030: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024040: 2020 2053 6361 6c61 7220 6c69 7465 7261 Scalar litera\n-00024050: 6c73 2e20 2020 2020 286c 696e 6520 2020 ls. (line \n-00024060: 3629 0a2a 2073 6361 6c61 7220 7265 6665 6).* scalar refe\n-00024070: 7265 6e63 653a 2020 2020 2020 2020 2020 rence: \n-00024080: 2020 2020 2020 2020 2020 2020 466f 726d Form\n-00024090: 7320 6f66 2072 6566 6572 656e 6365 732e s of references.\n-000240a0: 2028 6c69 6e65 2020 3133 290a 2a20 7363 (line 13).* sc\n-000240b0: 616c 6520 7472 616e 7366 6f72 6d3a 2020 ale transform: \n+00024040: 2053 6361 6c61 7220 6c69 7465 7261 6c73 Scalar literals\n+00024050: 2e20 2020 2020 286c 696e 6520 2020 3629 . (line 6)\n+00024060: 0a2a 2073 6361 6c61 7220 7265 6665 7265 .* scalar refere\n+00024070: 6e63 653a 2020 2020 2020 2020 2020 2020 nce: \n+00024080: 2020 2020 2020 2020 2020 466f 726d 7320 Forms \n+00024090: 6f66 2072 6566 6572 656e 6365 732e 2028 of references. (\n+000240a0: 6c69 6e65 2020 3133 290a 2a20 7363 616c line 13).* scal\n+000240b0: 6520 7472 616e 7366 6f72 6d3a 2020 2020 e transform: \n 000240c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000240d0: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-000240e0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n-000240f0: 2031 3629 0a2a 2073 6361 6c65 2074 7261 16).* scale tra\n-00024100: 6e73 666f 726d 203c 313e 3a20 2020 2020 nsform <1>: \n-00024110: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-00024120: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-00024130: 2e20 2028 6c69 6e65 2020 3137 290a 2a20 . (line 17).* \n-00024140: 7363 656e 6520 6465 7363 7269 7074 696f scene descriptio\n-00024150: 6e20 6c61 6e67 7561 6765 3a20 2020 2020 n language: \n-00024160: 2020 2020 2020 204c 616e 6775 6167 6520 Language \n-00024170: 6261 7369 6373 2e20 2020 2020 286c 696e basics. (lin\n-00024180: 6520 2020 3829 0a2a 2073 6365 6e65 2064 e 8).* scene d\n-00024190: 6573 6372 6970 7469 6f6e 206c 616e 6775 escription langu\n-000241a0: 6167 6520 3c31 3e3a 2020 2020 2020 2020 age <1>: \n-000241b0: 4275 696c 6469 6e67 2061 2064 7261 7769 Building a drawi\n-000241c0: 6e67 2e20 2028 6c69 6e65 2020 2037 290a ng. (line 7).\n-000241d0: 2a20 7363 6f70 652c 2069 6465 6e74 6966 * scope, identif\n-000241e0: 6965 723a 2020 2020 2020 2020 2020 2020 ier: \n-000241f0: 2020 2020 2020 2020 204f 626a 6563 7420 Object \n-00024200: 7472 616e 7366 6f72 6d73 2e20 2020 286c transforms. (l\n-00024210: 696e 6520 2032 3629 0a2a 2073 636f 7065 ine 26).* scope\n-00024220: 2c20 6964 656e 7469 6669 6572 203c 313e , identifier <1>\n-00024230: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00024240: 2020 426c 6f63 6b73 2e20 2020 2020 2020 Blocks. \n-00024250: 2020 2020 2020 2028 6c69 6e65 2020 3133 (line 13\n-00024260: 290a 2a20 7369 6d70 6c65 2064 6566 696e ).* simple defin\n-00024270: 6974 696f 6e3a 2020 2020 2020 2020 2020 ition: \n-00024280: 2020 2020 2020 2020 2020 2046 6f72 6d73 Forms\n-00024290: 206f 6620 6465 6669 6e69 7469 6f6e 732e of definitions.\n-000242a0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+000240d0: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+000240e0: 6572 616c 732e 2020 286c 696e 6520 2031 erals. (line 1\n+000240f0: 3629 0a2a 2073 6361 6c65 2074 7261 6e73 6).* scale trans\n+00024100: 666f 726d 203c 313e 3a20 2020 2020 2020 form <1>: \n+00024110: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+00024120: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+00024130: 2028 6c69 6e65 2020 3137 290a 2a20 7363 (line 17).* sc\n+00024140: 656e 6520 6465 7363 7269 7074 696f 6e20 ene description \n+00024150: 6c61 6e67 7561 6765 3a20 2020 2020 2020 language: \n+00024160: 2020 2020 204c 616e 6775 6167 6520 6261 Language ba\n+00024170: 7369 6373 2e20 2020 2020 286c 696e 6520 sics. (line \n+00024180: 2020 3829 0a2a 2073 6365 6e65 2064 6573 8).* scene des\n+00024190: 6372 6970 7469 6f6e 206c 616e 6775 6167 cription languag\n+000241a0: 6520 3c31 3e3a 2020 2020 2020 2020 4275 e <1>: Bu\n+000241b0: 696c 6469 6e67 2061 2064 7261 7769 6e67 ilding a drawing\n+000241c0: 2e20 2028 6c69 6e65 2020 2037 290a 2a20 . (line 7).* \n+000241d0: 7363 6f70 652c 2069 6465 6e74 6966 6965 scope, identifie\n+000241e0: 723a 2020 2020 2020 2020 2020 2020 2020 r: \n+000241f0: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n+00024200: 616e 7366 6f72 6d73 2e20 2020 286c 696e ansforms. (lin\n+00024210: 6520 2032 3629 0a2a 2073 636f 7065 2c20 e 26).* scope, \n+00024220: 6964 656e 7469 6669 6572 203c 313e 3a20 identifier <1>: \n+00024230: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024240: 426c 6f63 6b73 2e20 2020 2020 2020 2020 Blocks. \n+00024250: 2020 2020 2028 6c69 6e65 2020 3133 290a (line 13).\n+00024260: 2a20 7369 6d70 6c65 2064 6566 696e 6974 * simple definit\n+00024270: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n+00024280: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n+00024290: 6620 6465 6669 6e69 7469 6f6e 732e 0a20 f definitions.. \n+000242a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000242b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000242c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000242d0: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-000242e0: 6c69 6e65 2020 2036 290a 2a20 736f 6c69 line 6).* soli\n-000242f0: 643a 2020 2020 2020 2020 2020 2020 2020 d: \n+000242d0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+000242e0: 6e65 2020 2036 290a 2a20 736f 6c69 643a ne 6).* solid:\n+000242f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024310: 2020 2044 7261 7769 6e67 2061 2073 6f6c Drawing a sol\n-00024320: 6964 2e20 2020 2020 286c 696e 6520 2020 id. (line \n-00024330: 3629 0a2a 2073 7065 6369 616c 2061 7267 6).* special arg\n-00024340: 756d 656e 7420 7375 6273 7469 7475 7469 ument substituti\n-00024350: 6f6e 3a20 2020 2020 2020 2020 5370 6563 on: Spec\n-00024360: 6961 6c20 6f62 6a65 6374 732e 2020 2020 ial objects. \n-00024370: 2028 6c69 6e65 2020 3238 290a 2a20 7370 (line 28).* sp\n-00024380: 6563 6961 6c20 6172 6775 6d65 6e74 2073 ecial argument s\n-00024390: 7562 7374 6974 7574 696f 6e20 3c31 3e3a ubstitution <1>:\n-000243a0: 2020 2020 2053 7065 6369 616c 732e 2020 Specials. \n-000243b0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-000243c0: 2031 3029 0a2a 2073 7065 6369 616c 206f 10).* special o\n-000243d0: 626a 6563 743a 2020 2020 2020 2020 2020 bject: \n-000243e0: 2020 2020 2020 2020 2020 2020 2020 5370 Sp\n-000243f0: 6563 6961 6c20 6f62 6a65 6374 732e 2020 ecial objects. \n-00024400: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n-00024410: 7370 6563 6961 6c20 6f62 6a65 6374 733a special objects:\n+00024310: 2044 7261 7769 6e67 2061 2073 6f6c 6964 Drawing a solid\n+00024320: 2e20 2020 2020 286c 696e 6520 2020 3629 . (line 6)\n+00024330: 0a2a 2073 7065 6369 616c 2061 7267 756d .* special argum\n+00024340: 656e 7420 7375 6273 7469 7475 7469 6f6e ent substitution\n+00024350: 3a20 2020 2020 2020 2020 5370 6563 6961 : Specia\n+00024360: 6c20 6f62 6a65 6374 732e 2020 2020 2028 l objects. (\n+00024370: 6c69 6e65 2020 3238 290a 2a20 7370 6563 line 28).* spec\n+00024380: 6961 6c20 6172 6775 6d65 6e74 2073 7562 ial argument sub\n+00024390: 7374 6974 7574 696f 6e20 3c31 3e3a 2020 stitution <1>: \n+000243a0: 2020 2053 7065 6369 616c 732e 2020 2020 Specials. \n+000243b0: 2020 2020 2020 2020 286c 696e 6520 2031 (line 1\n+000243c0: 3029 0a2a 2073 7065 6369 616c 206f 626a 0).* special obj\n+000243d0: 6563 743a 2020 2020 2020 2020 2020 2020 ect: \n+000243e0: 2020 2020 2020 2020 2020 2020 5370 6563 Spec\n+000243f0: 6961 6c20 6f62 6a65 6374 732e 2020 2020 ial objects. \n+00024400: 2028 6c69 6e65 2020 2036 290a 2a20 7370 (line 6).* sp\n+00024410: 6563 6961 6c20 6f62 6a65 6374 733a 2020 ecial objects: \n 00024420: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024430: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n-00024440: 616c 2064 7261 7769 6e67 2e20 286c 696e al drawing. (lin\n-00024450: 6520 2033 3829 0a2a 2073 706c 6974 7469 e 38).* splitti\n-00024460: 6e67 2c20 6c69 6e65 2061 6e64 2073 7572 ng, line and sur\n-00024470: 6661 6365 3a20 2020 2020 2020 2020 2020 face: \n-00024480: 4865 6c6c 6f20 776f 726c 642e 2020 2020 Hello world. \n-00024490: 2020 2020 2028 6c69 6e65 2020 3139 290a (line 19).\n-000244a0: 2a20 7370 6c69 7474 696e 672c 206c 696e * splitting, lin\n-000244b0: 6520 616e 6420 7375 7266 6163 6520 3c31 e and surface <1\n-000244c0: 3e3a 2020 2020 2020 2048 6964 6465 6e20 >: Hidden \n-000244d0: 7375 7266 6163 6520 7265 6d6f 7661 6c2e surface removal.\n-000244e0: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+00024430: 2020 2020 2041 2074 6563 686e 6963 616c A technical\n+00024440: 2064 7261 7769 6e67 2e20 286c 696e 6520 drawing. (line \n+00024450: 2033 3829 0a2a 2073 706c 6974 7469 6e67 38).* splitting\n+00024460: 2c20 6c69 6e65 2061 6e64 2073 7572 6661 , line and surfa\n+00024470: 6365 3a20 2020 2020 2020 2020 2020 4865 ce: He\n+00024480: 6c6c 6f20 776f 726c 642e 2020 2020 2020 llo world. \n+00024490: 2020 2028 6c69 6e65 2020 3139 290a 2a20 (line 19).* \n+000244a0: 7370 6c69 7474 696e 672c 206c 696e 6520 splitting, line \n+000244b0: 616e 6420 7375 7266 6163 6520 3c31 3e3a and surface <1>:\n+000244c0: 2020 2020 2020 2048 6964 6465 6e20 7375 Hidden su\n+000244d0: 7266 6163 6520 7265 6d6f 7661 6c2e 0a20 rface removal.. \n+000244e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000244f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024500: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024510: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-00024520: 6c69 6e65 2020 3231 290a 2a20 7375 6273 line 21).* subs\n-00024530: 7469 7475 7469 6f6e 2c20 7370 6563 6961 titution, specia\n-00024540: 6c3a 2020 2020 2020 2020 2020 2020 2020 l: \n-00024550: 2020 2053 7065 6369 616c 206f 626a 6563 Special objec\n-00024560: 7473 2e20 2020 2020 286c 696e 6520 2032 ts. (line 2\n-00024570: 3829 0a2a 2073 7572 6661 6365 3a20 2020 8).* surface: \n+00024510: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+00024520: 6e65 2020 3231 290a 2a20 7375 6273 7469 ne 21).* substi\n+00024530: 7475 7469 6f6e 2c20 7370 6563 6961 6c3a tution, special:\n+00024540: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024550: 2053 7065 6369 616c 206f 626a 6563 7473 Special objects\n+00024560: 2e20 2020 2020 286c 696e 6520 2032 3829 . (line 28)\n+00024570: 0a2a 2073 7572 6661 6365 3a20 2020 2020 .* surface: \n 00024580: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024590: 2020 2020 2020 2020 2020 2020 506f 6c79 Poly\n-000245a0: 6c69 6e65 2073 7765 6570 732e 2020 2020 line sweeps. \n-000245b0: 2028 6c69 6e65 2020 2036 290a 2a20 7377 (line 6).* sw\n-000245c0: 6565 703a 2020 2020 2020 2020 2020 2020 eep: \n+00024590: 2020 2020 2020 2020 2020 506f 6c79 6c69 Polyli\n+000245a0: 6e65 2073 7765 6570 732e 2020 2020 2028 ne sweeps. (\n+000245b0: 6c69 6e65 2020 2036 290a 2a20 7377 6565 line 6).* swee\n+000245c0: 703a 2020 2020 2020 2020 2020 2020 2020 p: \n 000245d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000245e0: 2020 2020 2053 7765 7074 206f 626a 6563 Swept objec\n-000245f0: 7473 2e20 2020 2020 2020 286c 696e 6520 ts. (line \n-00024600: 2020 3629 0a2a 2073 7765 7074 2062 6f63 6).* swept boc\n-00024610: 6b3a 2020 2020 2020 2020 2020 2020 2020 k: \n-00024620: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n-00024630: 6570 7420 626c 6f63 6b73 2e20 2020 2020 ept blocks. \n-00024640: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n-00024650: 7377 6570 7420 6c69 6e65 3a20 2020 2020 swept line: \n+000245e0: 2020 2053 7765 7074 206f 626a 6563 7473 Swept objects\n+000245f0: 2e20 2020 2020 2020 286c 696e 6520 2020 . (line \n+00024600: 3629 0a2a 2073 7765 7074 2062 6f63 6b3a 6).* swept bock:\n+00024610: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024620: 2020 2020 2020 2020 2020 2020 5377 6570 Swep\n+00024630: 7420 626c 6f63 6b73 2e20 2020 2020 2020 t blocks. \n+00024640: 2028 6c69 6e65 2020 2036 290a 2a20 7377 (line 6).* sw\n+00024650: 6570 7420 6c69 6e65 3a20 2020 2020 2020 ept line: \n 00024660: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024670: 2020 2020 2020 2050 6f6c 796c 696e 6520 Polyline \n-00024680: 7377 6565 7073 2e20 2020 2020 286c 696e sweeps. (lin\n-00024690: 6520 2020 3629 0a2a 2073 7765 7074 206c e 6).* swept l\n-000246a0: 696e 6520 3c31 3e3a 2020 2020 2020 2020 ine <1>: \n-000246b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000246c0: 5377 6570 7420 6c69 6e65 732e 2020 2020 Swept lines. \n-000246d0: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n-000246e0: 2a20 7377 6570 7420 6c69 6e65 203c 323e * swept line <2>\n-000246f0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00024700: 2020 2020 2020 2020 2041 2074 6563 686e A techn\n-00024710: 6963 616c 2064 7261 7769 6e67 2e20 286c ical drawing. (l\n-00024720: 696e 6520 2032 3029 0a2a 2073 7765 7074 ine 20).* swept\n-00024730: 206f 626a 6563 743a 2020 2020 2020 2020 object: \n+00024670: 2020 2020 2050 6f6c 796c 696e 6520 7377 Polyline sw\n+00024680: 6565 7073 2e20 2020 2020 286c 696e 6520 eeps. (line \n+00024690: 2020 3629 0a2a 2073 7765 7074 206c 696e 6).* swept lin\n+000246a0: 6520 3c31 3e3a 2020 2020 2020 2020 2020 e <1>: \n+000246b0: 2020 2020 2020 2020 2020 2020 2020 5377 Sw\n+000246c0: 6570 7420 6c69 6e65 732e 2020 2020 2020 ept lines. \n+000246d0: 2020 2028 6c69 6e65 2020 2036 290a 2a20 (line 6).* \n+000246e0: 7377 6570 7420 6c69 6e65 203c 323e 3a20 swept line <2>: \n+000246f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00024700: 2020 2020 2020 2041 2074 6563 686e 6963 A technic\n+00024710: 616c 2064 7261 7769 6e67 2e20 286c 696e al drawing. (lin\n+00024720: 6520 2032 3029 0a2a 2073 7765 7074 206f e 20).* swept o\n+00024730: 626a 6563 743a 2020 2020 2020 2020 2020 bject: \n 00024740: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024750: 2020 5377 6570 7420 6f62 6a65 6374 732e Swept objects.\n-00024760: 2020 2020 2020 2028 6c69 6e65 2020 2036 (line 6\n-00024770: 290a 2a20 7377 6570 7420 6f62 6a65 6374 ).* swept object\n-00024780: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-00024790: 2020 2020 2020 2020 2020 2053 7765 6570 Sweep\n-000247a0: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n-000247b0: 286c 696e 6520 2020 3929 0a2a 2073 7765 (line 9).* swe\n-000247c0: 7074 2070 6f69 6e74 3a20 2020 2020 2020 pt point: \n+00024750: 5377 6570 7420 6f62 6a65 6374 732e 2020 Swept objects. \n+00024760: 2020 2020 2028 6c69 6e65 2020 2036 290a (line 6).\n+00024770: 2a20 7377 6570 7420 6f62 6a65 6374 203c * swept object <\n+00024780: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+00024790: 2020 2020 2020 2020 2053 7765 6570 732e Sweeps.\n+000247a0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+000247b0: 696e 6520 2020 3929 0a2a 2073 7765 7074 ine 9).* swept\n+000247c0: 2070 6f69 6e74 3a20 2020 2020 2020 2020 point: \n 000247d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000247e0: 2020 2020 5377 6570 7420 6f62 6a65 6374 Swept object\n-000247f0: 732e 2020 2020 2020 2028 6c69 6e65 2020 s. 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(line \n+00024890: 2036 290a 2a20 7377 6570 7420 706f 6c79 6).* swept poly\n+000248a0: 676f 6e20 3c31 3e3a 2020 2020 2020 2020 gon <1>: \n+000248b0: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+000248c0: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+000248d0: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 000248e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000248f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024900: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024910: 2020 2028 6c69 6e65 2031 3232 290a 2a20 (line 122).* \n-00024920: 7461 6720 6465 6669 6e69 7469 6f6e 3a20 tag definition: \n+00024910: 2028 6c69 6e65 2031 3232 290a 2a20 7461 (line 122).* ta\n+00024920: 6720 6465 6669 6e69 7469 6f6e 3a20 2020 g definition: \n 00024930: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024940: 2020 2020 2020 2044 6566 696e 6974 696f Definitio\n-00024950: 6e73 2e20 2020 2020 2020 2020 286c 696e ns. (lin\n-00024960: 6520 2031 3829 0a2a 2074 6167 2064 6566 e 18).* tag def\n-00024970: 696e 6974 696f 6e20 3c31 3e3a 2020 2020 inition <1>: \n-00024980: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024990: 466f 726d 7320 6f66 2064 6566 696e 6974 Forms of definit\n-000249a0: 696f 6e73 2e0a 2020 2020 2020 2020 2020 ions.. \n+00024940: 2020 2020 2044 6566 696e 6974 696f 6e73 Definitions\n+00024950: 2e20 2020 2020 2020 2020 286c 696e 6520 . (line \n+00024960: 2031 3829 0a2a 2074 6167 2064 6566 696e 18).* tag defin\n+00024970: 6974 696f 6e20 3c31 3e3a 2020 2020 2020 ition <1>: \n+00024980: 2020 2020 2020 2020 2020 2020 2020 466f Fo\n+00024990: 726d 7320 6f66 2064 6566 696e 6974 696f rms of definitio\n+000249a0: 6e73 2e0a 2020 2020 2020 2020 2020 2020 ns.. \n 000249b0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000249c0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000249d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000249e0: 2020 2020 286c 696e 6520 2020 3729 0a2a (line 7).*\n-000249f0: 2074 6167 2064 6566 696e 6974 696f 6e20 tag definition \n-00024a00: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n-00024a10: 2020 2020 2020 2020 436f 6d6d 616e 6420 Command \n-00024a20: 6c69 6e65 2e20 2020 2020 2020 2028 6c69 line. (li\n-00024a30: 6e65 2020 3533 290a 2a20 7461 6720 7265 ne 53).* tag re\n-00024a40: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n-00024a50: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024a60: 2046 6f72 6d73 206f 6620 6465 6669 6e69 Forms of defini\n-00024a70: 7469 6f6e 732e 0a20 2020 2020 2020 2020 tions.. \n+000249e0: 2020 286c 696e 6520 2020 3729 0a2a 2074 (line 7).* t\n+000249f0: 6167 2064 6566 696e 6974 696f 6e20 3c32 ag definition <2\n+00024a00: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00024a10: 2020 2020 2020 436f 6d6d 616e 6420 6c69 Command li\n+00024a20: 6e65 2e20 2020 2020 2020 2028 6c69 6e65 ne. (line\n+00024a30: 2020 3533 290a 2a20 7461 6720 7265 6665 53).* tag refe\n+00024a40: 7265 6e63 653a 2020 2020 2020 2020 2020 rence: \n+00024a50: 2020 2020 2020 2020 2020 2020 2020 2046 F\n+00024a60: 6f72 6d73 206f 6620 6465 6669 6e69 7469 orms of definiti\n+00024a70: 6f6e 732e 0a20 2020 2020 2020 2020 2020 ons.. \n 00024a80: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024a90: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024aa0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024ab0: 2020 2020 2028 6c69 6e65 2020 3230 290a (line 20).\n-00024ac0: 2a20 7461 6720 7265 6665 7265 6e63 6520 * tag reference \n-00024ad0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00024ae0: 2020 2020 2020 2020 2046 6f72 6d73 206f Forms o\n-00024af0: 6620 7265 6665 7265 6e63 6573 2e20 286c f references. (l\n-00024b00: 696e 6520 2031 3929 0a2a 2074 656d 706c ine 19).* templ\n-00024b10: 6174 652c 2064 6f63 756d 656e 743a 2020 ate, document: \n+00024ab0: 2020 2028 6c69 6e65 2020 3230 290a 2a20 (line 20).* \n+00024ac0: 7461 6720 7265 6665 7265 6e63 6520 3c31 tag reference <1\n+00024ad0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00024ae0: 2020 2020 2020 2046 6f72 6d73 206f 6620 Forms of \n+00024af0: 7265 6665 7265 6e63 6573 2e20 286c 696e references. (lin\n+00024b00: 6520 2031 3929 0a2a 2074 656d 706c 6174 e 19).* templat\n+00024b10: 652c 2064 6f63 756d 656e 743a 2020 2020 e, document: \n 00024b20: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024b30: 2020 4865 6c6c 6f20 776f 726c 642e 2020 Hello world. \n-00024b40: 2020 2020 2020 2028 6c69 6e65 2020 3332 (line 32\n-00024b50: 290a 2a20 7465 6d70 6c61 7465 2c20 646f ).* template, do\n-00024b60: 6375 6d65 6e74 203c 313e 3a20 2020 2020 cument <1>: \n-00024b70: 2020 2020 2020 2020 2020 2043 6f6d 6d61 Comma\n-00024b80: 6e64 206c 696e 652e 2020 2020 2020 2020 nd line. \n-00024b90: 286c 696e 6520 2033 3629 0a2a 2074 6574 (line 36).* tet\n-00024ba0: 7261 6865 6472 6f6e 3a20 2020 2020 2020 rahedron: \n+00024b30: 4865 6c6c 6f20 776f 726c 642e 2020 2020 Hello world. \n+00024b40: 2020 2020 2028 6c69 6e65 2020 3332 290a (line 32).\n+00024b50: 2a20 7465 6d70 6c61 7465 2c20 646f 6375 * template, docu\n+00024b60: 6d65 6e74 203c 313e 3a20 2020 2020 2020 ment <1>: \n+00024b70: 2020 2020 2020 2020 2043 6f6d 6d61 6e64 Command\n+00024b80: 206c 696e 652e 2020 2020 2020 2020 286c line. (l\n+00024b90: 696e 6520 2033 3629 0a2a 2074 6574 7261 ine 36).* tetra\n+00024ba0: 6865 6472 6f6e 3a20 2020 2020 2020 2020 hedron: \n 00024bb0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024bc0: 2020 2020 4472 6177 696e 6720 6120 736f Drawing a so\n-00024bd0: 6c69 642e 2020 2020 2028 6c69 6e65 2020 lid. (line \n-00024be0: 2039 290a 2a20 7469 636b 206f 7065 7261 9).* tick opera\n-00024bf0: 746f 7220 2827 293a 2020 2020 2020 2020 tor ('): \n-00024c00: 2020 2020 2020 2020 2020 2020 2041 6666 Aff\n-00024c10: 696e 6520 6172 6974 686d 6574 6963 2e20 ine arithmetic. \n-00024c20: 2020 286c 696e 6520 2033 3729 0a2a 2074 (line 37).* t\n-00024c30: 6963 6b20 6f70 6572 6174 6f72 2028 2729 ick operator (')\n-00024c40: 203c 313e 3a20 2020 2020 2020 2020 2020 <1>: \n-00024c50: 2020 2020 2020 5477 6f2d 6f70 6572 616e Two-operan\n-00024c60: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n-00024c70: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n+00024bc0: 2020 4472 6177 696e 6720 6120 736f 6c69 Drawing a soli\n+00024bd0: 642e 2020 2020 2028 6c69 6e65 2020 2039 d. (line 9\n+00024be0: 290a 2a20 7469 636b 206f 7065 7261 746f ).* tick operato\n+00024bf0: 7220 2827 293a 2020 2020 2020 2020 2020 r ('): \n+00024c00: 2020 2020 2020 2020 2020 2041 6666 696e Affin\n+00024c10: 6520 6172 6974 686d 6574 6963 2e20 2020 e arithmetic. \n+00024c20: 286c 696e 6520 2033 3729 0a2a 2074 6963 (line 37).* tic\n+00024c30: 6b20 6f70 6572 6174 6f72 2028 2729 203c k operator (') <\n+00024c40: 313e 3a20 2020 2020 2020 2020 2020 2020 1>: \n+00024c50: 2020 2020 5477 6f2d 6f70 6572 616e 6420 Two-operand \n+00024c60: 2862 696e 6172 7929 2066 6f72 6d73 2e0a (binary) forms..\n+00024c70: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024c80: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024c90: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024ca0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024cb0: 286c 696e 6520 2034 3129 0a2a 2054 696b (line 41).* Tik\n-00024cc0: 5a2f 5047 463a 2020 2020 2020 2020 2020 Z/PGF: \n+00024ca0: 2020 2020 2020 2020 2020 2020 2020 286c (l\n+00024cb0: 696e 6520 2034 3129 0a2a 2054 696b 5a2f ine 41).* TikZ/\n+00024cc0: 5047 463a 2020 2020 2020 2020 2020 2020 PGF: \n 00024cd0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024ce0: 2020 2020 4162 6f75 7420 736b 6574 6368 About sketch\n-00024cf0: 2e20 2020 2020 2020 2028 6c69 6e65 2020 . (line \n-00024d00: 3232 290a 2a20 746f 726f 6964 3a20 2020 22).* toroid: \n+00024ce0: 2020 4162 6f75 7420 736b 6574 6368 2e20 About sketch. \n+00024cf0: 2020 2020 2020 2028 6c69 6e65 2020 3232 (line 22\n+00024d00: 290a 2a20 746f 726f 6964 3a20 2020 2020 ).* toroid: \n 00024d10: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024d20: 2020 2020 2020 2020 2020 2020 204e 6573 Nes\n-00024d30: 7465 6420 7377 6565 7073 2e20 2020 2020 ted sweeps. \n-00024d40: 2020 286c 696e 6520 2020 3829 0a2a 2074 (line 8).* t\n-00024d50: 7261 6e73 666f 726d 3a20 2020 2020 2020 ransform: \n+00024d20: 2020 2020 2020 2020 2020 204e 6573 7465 Neste\n+00024d30: 6420 7377 6565 7073 2e20 2020 2020 2020 d sweeps. \n+00024d40: 286c 696e 6520 2020 3829 0a2a 2074 7261 (line 8).* tra\n+00024d50: 6e73 666f 726d 3a20 2020 2020 2020 2020 nsform: \n 00024d60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024d70: 2020 2020 2020 4f62 6a65 6374 2074 7261 Object tra\n-00024d80: 6e73 666f 726d 732e 2020 2028 6c69 6e65 nsforms. (line\n-00024d90: 2020 2036 290a 2a20 7472 616e 7366 6f72 6).* transfor\n-00024da0: 6d20 3c31 3e3a 2020 2020 2020 2020 2020 m <1>: \n-00024db0: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-00024dc0: 776f 2d6f 7065 7261 6e64 2028 6269 6e61 wo-operand (bina\n-00024dd0: 7279 2920 666f 726d 732e 0a20 2020 2020 ry) forms.. \n+00024d70: 2020 2020 4f62 6a65 6374 2074 7261 6e73 Object trans\n+00024d80: 666f 726d 732e 2020 2028 6c69 6e65 2020 forms. (line \n+00024d90: 2036 290a 2a20 7472 616e 7366 6f72 6d20 6).* transform \n+00024da0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n+00024db0: 2020 2020 2020 2020 2020 2020 2054 776f Two\n+00024dc0: 2d6f 7065 7261 6e64 2028 6269 6e61 7279 -operand (binary\n+00024dd0: 2920 666f 726d 732e 0a20 2020 2020 2020 ) forms.. \n 00024de0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024df0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00024e00: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024e10: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n-00024e20: 3238 290a 2a20 7472 616e 7366 6f72 6d20 28).* transform \n-00024e30: 3c32 3e3a 2020 2020 2020 2020 2020 2020 <2>: \n-00024e40: 2020 2020 2020 2020 2020 2020 2053 7765 Swe\n-00024e50: 6570 732e 2020 2020 2020 2020 2020 2020 eps. \n-00024e60: 2020 286c 696e 6520 2031 3129 0a2a 2074 (line 11).* t\n-00024e70: 7261 6e73 666f 726d 203c 333e 3a20 2020 ransform <3>: \n+00024e10: 2020 2020 2020 2028 6c69 6e65 2020 3238 (line 28\n+00024e20: 290a 2a20 7472 616e 7366 6f72 6d20 3c32 ).* transform <2\n+00024e30: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00024e40: 2020 2020 2020 2020 2020 2053 7765 6570 Sweep\n+00024e50: 732e 2020 2020 2020 2020 2020 2020 2020 s. \n+00024e60: 286c 696e 6520 2031 3129 0a2a 2074 7261 (line 11).* tra\n+00024e70: 6e73 666f 726d 203c 333e 3a20 2020 2020 nsform <3>: \n 00024e80: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024e90: 2020 2020 2020 5265 7065 6174 732e 2020 Repeats. \n-00024ea0: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00024eb0: 2020 2039 290a 2a20 7472 616e 7366 6f72 9).* transfor\n-00024ec0: 6d20 3c34 3e3a 2020 2020 2020 2020 2020 m <4>: \n-00024ed0: 2020 2020 2020 2020 2020 2020 2020 204f O\n-00024ee0: 7665 7276 6965 772e 2020 2020 2020 2020 verview. \n-00024ef0: 2020 2020 286c 696e 6520 2020 3729 0a2a (line 7).*\n-00024f00: 2074 7261 6e73 666f 726d 2064 6566 696e transform defin\n-00024f10: 6974 696f 6e3a 2020 2020 2020 2020 2020 ition: \n-00024f20: 2020 2020 2020 2020 4f76 6572 7669 6577 Overview\n-00024f30: 2e20 2020 2020 2020 2020 2020 2028 6c69 . (li\n-00024f40: 6e65 2020 3335 290a 2a20 7472 616e 7366 ne 35).* transf\n-00024f50: 6f72 6d20 6c69 7465 7261 6c3a 2020 2020 orm literal: \n-00024f60: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00024f70: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n-00024f80: 616c 732e 2020 286c 696e 6520 2020 3629 als. (line 6)\n-00024f90: 0a2a 2074 7261 6e73 666f 726d 2072 6566 .* transform ref\n-00024fa0: 6572 656e 6365 3a20 2020 2020 2020 2020 erence: \n-00024fb0: 2020 2020 2020 2020 2020 466f 726d 7320 Forms \n-00024fc0: 6f66 2072 6566 6572 656e 6365 732e 2028 of references. (\n-00024fd0: 6c69 6e65 2020 3136 290a 2a20 7472 616e line 16).* tran\n-00024fe0: 7366 6f72 6d20 7265 6665 7265 6e63 6520 sform reference \n-00024ff0: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00025000: 2020 204f 7665 7276 6965 772e 2020 2020 Overview. \n-00025010: 2020 2020 2020 2020 286c 696e 6520 2033 (line 3\n-00025020: 3529 0a2a 2074 7261 6e73 666f 726d 2c20 5).* transform, \n-00025030: 6469 7265 6374 3a20 2020 2020 2020 2020 direct: \n-00025040: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n-00025050: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-00025060: 2028 6c69 6e65 2020 3437 290a 2a20 7472 (line 47).* tr\n-00025070: 616e 7366 6f72 6d2c 2064 6972 6563 7420 ansform, direct \n-00025080: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00025090: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n-000250a0: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n-000250b0: 2035 3329 0a2a 2074 7261 6e73 666f 726d 53).* transform\n-000250c0: 2c20 726f 7461 7469 6f6e 3a20 2020 2020 , rotation: \n-000250d0: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n-000250e0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-000250f0: 2e20 2028 6c69 6e65 2020 3130 290a 2a20 . (line 10).* \n-00025100: 7472 616e 7366 6f72 6d2c 2072 6f74 6174 transform, rotat\n-00025110: 696f 6e20 3c31 3e3a 2020 2020 2020 2020 ion <1>: \n-00025120: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n-00025130: 6869 6361 6c20 6d6f 6465 6c2e 0a20 2020 hical model.. \n+00024e90: 2020 2020 5265 7065 6174 732e 2020 2020 Repeats. \n+00024ea0: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00024eb0: 2039 290a 2a20 7472 616e 7366 6f72 6d20 9).* transform \n+00024ec0: 3c34 3e3a 2020 2020 2020 2020 2020 2020 <4>: \n+00024ed0: 2020 2020 2020 2020 2020 2020 204f 7665 Ove\n+00024ee0: 7276 6965 772e 2020 2020 2020 2020 2020 rview. \n+00024ef0: 2020 286c 696e 6520 2020 3729 0a2a 2074 (line 7).* t\n+00024f00: 7261 6e73 666f 726d 2064 6566 696e 6974 ransform definit\n+00024f10: 696f 6e3a 2020 2020 2020 2020 2020 2020 ion: \n+00024f20: 2020 2020 2020 4f76 6572 7669 6577 2e20 Overview. \n+00024f30: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n+00024f40: 2020 3335 290a 2a20 7472 616e 7366 6f72 35).* transfor\n+00024f50: 6d20 6c69 7465 7261 6c3a 2020 2020 2020 m literal: \n+00024f60: 2020 2020 2020 2020 2020 2020 2020 2054 T\n+00024f70: 7261 6e73 666f 726d 206c 6974 6572 616c ransform literal\n+00024f80: 732e 2020 286c 696e 6520 2020 3629 0a2a s. (line 6).*\n+00024f90: 2074 7261 6e73 666f 726d 2072 6566 6572 transform refer\n+00024fa0: 656e 6365 3a20 2020 2020 2020 2020 2020 ence: \n+00024fb0: 2020 2020 2020 2020 466f 726d 7320 6f66 Forms of\n+00024fc0: 2072 6566 6572 656e 6365 732e 2028 6c69 references. (li\n+00024fd0: 6e65 2020 3136 290a 2a20 7472 616e 7366 ne 16).* transf\n+00024fe0: 6f72 6d20 7265 6665 7265 6e63 6520 3c31 orm reference <1\n+00024ff0: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00025000: 204f 7665 7276 6965 772e 2020 2020 2020 Overview. \n+00025010: 2020 2020 2020 286c 696e 6520 2033 3529 (line 35)\n+00025020: 0a2a 2074 7261 6e73 666f 726d 2c20 6469 .* transform, di\n+00025030: 7265 6374 3a20 2020 2020 2020 2020 2020 rect: \n+00025040: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+00025050: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028 orm literals. (\n+00025060: 6c69 6e65 2020 3437 290a 2a20 7472 616e line 47).* tran\n+00025070: 7366 6f72 6d2c 2064 6972 6563 7420 3c31 sform, direct <1\n+00025080: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00025090: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n+000250a0: 6572 616c 732e 2020 286c 696e 6520 2035 erals. (line 5\n+000250b0: 3329 0a2a 2074 7261 6e73 666f 726d 2c20 3).* transform, \n+000250c0: 726f 7461 7469 6f6e 3a20 2020 2020 2020 rotation: \n+000250d0: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+000250e0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+000250f0: 2028 6c69 6e65 2020 3130 290a 2a20 7472 (line 10).* tr\n+00025100: 616e 7366 6f72 6d2c 2072 6f74 6174 696f ansform, rotatio\n+00025110: 6e20 3c31 3e3a 2020 2020 2020 2020 2020 n <1>: \n+00025120: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n+00025130: 6361 6c20 6d6f 6465 6c2e 0a20 2020 2020 cal model.. \n 00025140: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025150: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025160: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025170: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00025180: 2020 3438 290a 2a20 7472 616e 7366 6f72 48).* transfor\n-00025190: 6d2c 2072 6f74 6174 696f 6e20 3c32 3e3a m, rotation <2>:\n-000251a0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-000251b0: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-000251c0: 6465 6c2e 0a20 2020 2020 2020 2020 2020 del.. \n+00025170: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00025180: 3438 290a 2a20 7472 616e 7366 6f72 6d2c 48).* transform,\n+00025190: 2072 6f74 6174 696f 6e20 3c32 3e3a 2020 rotation <2>: \n+000251a0: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+000251b0: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+000251c0: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 000251d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000251e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000251f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025200: 2020 2028 6c69 6e65 2020 3538 290a 2a20 (line 58).* \n-00025210: 7472 616e 7366 6f72 6d2c 2072 6f74 6174 transform, rotat\n-00025220: 696f 6e20 3c33 3e3a 2020 2020 2020 2020 ion <3>: \n-00025230: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n-00025240: 6869 6361 6c20 6d6f 6465 6c2e 0a20 2020 hical model.. \n+00025200: 2028 6c69 6e65 2020 3538 290a 2a20 7472 (line 58).* tr\n+00025210: 616e 7366 6f72 6d2c 2072 6f74 6174 696f ansform, rotatio\n+00025220: 6e20 3c33 3e3a 2020 2020 2020 2020 2020 n <3>: \n+00025230: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n+00025240: 6361 6c20 6d6f 6465 6c2e 0a20 2020 2020 cal model.. \n 00025250: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025260: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025270: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025280: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00025290: 2020 3738 290a 2a20 7472 616e 7366 6f72 78).* transfor\n-000252a0: 6d2c 2072 6f74 6174 696f 6e20 3c34 3e3a m, rotation <4>:\n-000252b0: 2020 2020 2020 2020 2020 2020 2020 2041 A\n-000252c0: 2068 6965 7261 7263 6869 6361 6c20 6d6f hierarchical mo\n-000252d0: 6465 6c2e 0a20 2020 2020 2020 2020 2020 del.. \n+00025280: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00025290: 3738 290a 2a20 7472 616e 7366 6f72 6d2c 78).* transform,\n+000252a0: 2072 6f74 6174 696f 6e20 3c34 3e3a 2020 rotation <4>: \n+000252b0: 2020 2020 2020 2020 2020 2020 2041 2068 A h\n+000252c0: 6965 7261 7263 6869 6361 6c20 6d6f 6465 ierarchical mode\n+000252d0: 6c2e 0a20 2020 2020 2020 2020 2020 2020 l.. \n 000252e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000252f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025300: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025310: 2020 2028 6c69 6e65 2020 3933 290a 2a20 (line 93).* \n-00025320: 7472 616e 7366 6f72 6d2c 2073 6361 6c65 transform, scale\n-00025330: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-00025340: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-00025350: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-00025360: 6520 2031 3629 0a2a 2074 7261 6e73 666f e 16).* transfo\n-00025370: 726d 2c20 7363 616c 6520 3c31 3e3a 2020 rm, scale <1>: \n-00025380: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025390: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-000253a0: 6c73 2e20 2028 6c69 6e65 2020 3137 290a ls. (line 17).\n-000253b0: 2a20 7472 616e 7366 6f72 6d2c 2074 7261 * transform, tra\n-000253c0: 6e73 6c61 7469 6f6e 3a20 2020 2020 2020 nslation: \n-000253d0: 2020 2020 2020 2020 204f 626a 6563 7420 Object \n-000253e0: 7472 616e 7366 6f72 6d73 2e20 2020 286c transforms. (l\n-000253f0: 696e 6520 2034 3729 0a2a 2074 7261 6e73 ine 47).* trans\n-00025400: 666f 726d 2c20 7472 616e 736c 6174 696f form, translatio\n-00025410: 6e20 3c31 3e3a 2020 2020 2020 2020 2020 n <1>: \n-00025420: 2020 5472 616e 7366 6f72 6d20 6c69 7465 Transform lite\n-00025430: 7261 6c73 2e20 2028 6c69 6e65 2020 3135 rals. (line 15\n-00025440: 290a 2a20 7472 616e 7366 6f72 6d2c 2074 ).* transform, t\n-00025450: 7261 6e73 6c61 7469 6f6e 203c 323e 3a20 ranslation <2>: \n-00025460: 2020 2020 2020 2020 2020 2041 2068 6965 A hie\n-00025470: 7261 7263 6869 6361 6c20 6d6f 6465 6c2e rarchical model.\n-00025480: 0a20 2020 2020 2020 2020 2020 2020 2020 . \n+00025310: 2028 6c69 6e65 2020 3933 290a 2a20 7472 (line 93).* tr\n+00025320: 616e 7366 6f72 6d2c 2073 6361 6c65 3a20 ansform, scale: \n+00025330: 2020 2020 2020 2020 2020 2020 2020 2020 \n+00025340: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+00025350: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+00025360: 2031 3629 0a2a 2074 7261 6e73 666f 726d 16).* transform\n+00025370: 2c20 7363 616c 6520 3c31 3e3a 2020 2020 , scale <1>: \n+00025380: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n+00025390: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+000253a0: 2e20 2028 6c69 6e65 2020 3137 290a 2a20 . (line 17).* \n+000253b0: 7472 616e 7366 6f72 6d2c 2074 7261 6e73 transform, trans\n+000253c0: 6c61 7469 6f6e 3a20 2020 2020 2020 2020 lation: \n+000253d0: 2020 2020 2020 204f 626a 6563 7420 7472 Object tr\n+000253e0: 616e 7366 6f72 6d73 2e20 2020 286c 696e ansforms. (lin\n+000253f0: 6520 2034 3729 0a2a 2074 7261 6e73 666f e 47).* transfo\n+00025400: 726d 2c20 7472 616e 736c 6174 696f 6e20 rm, translation \n+00025410: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n+00025420: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n+00025430: 6c73 2e20 2028 6c69 6e65 2020 3135 290a ls. (line 15).\n+00025440: 2a20 7472 616e 7366 6f72 6d2c 2074 7261 * transform, tra\n+00025450: 6e73 6c61 7469 6f6e 203c 323e 3a20 2020 nslation <2>: \n+00025460: 2020 2020 2020 2020 2041 2068 6965 7261 A hiera\n+00025470: 7263 6869 6361 6c20 6d6f 6465 6c2e 0a20 rchical model.. \n+00025480: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025490: 2020 2020 2020 2020 2020 2020 2020 2020 \n 000254a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000254b0: 2020 2020 2020 2020 2020 2020 2020 2028 (\n-000254c0: 6c69 6e65 2020 3437 290a 2a20 7472 616e line 47).* tran\n-000254d0: 7366 6f72 6d2c 2076 6965 773a 2020 2020 sform, view: \n+000254b0: 2020 2020 2020 2020 2020 2020 2028 6c69 (li\n+000254c0: 6e65 2020 3437 290a 2a20 7472 616e 7366 ne 47).* transf\n+000254d0: 6f72 6d2c 2076 6965 773a 2020 2020 2020 orm, view: \n 000254e0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000254f0: 2020 2054 7261 6e73 666f 726d 206c 6974 Transform lit\n-00025500: 6572 616c 732e 2020 286c 696e 6520 2032 erals. (line 2\n-00025510: 3529 0a2a 2074 7261 6e73 666f 726d 2c20 5).* transform, \n-00025520: 7669 6577 203c 313e 3a20 2020 2020 2020 view <1>: \n-00025530: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n-00025540: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n-00025550: 2028 6c69 6e65 2020 3335 290a 2a20 7472 (line 35).* tr\n-00025560: 616e 736c 6174 696f 6e20 7472 616e 7366 anslation transf\n-00025570: 6f72 6d3a 2020 2020 2020 2020 2020 2020 orm: \n-00025580: 2020 2020 204f 626a 6563 7420 7472 616e Object tran\n-00025590: 7366 6f72 6d73 2e20 2020 286c 696e 6520 sforms. (line \n-000255a0: 2034 3729 0a2a 2074 7261 6e73 6c61 7469 47).* translati\n-000255b0: 6f6e 2074 7261 6e73 666f 726d 203c 313e on transform <1>\n-000255c0: 3a20 2020 2020 2020 2020 2020 2020 5472 : Tr\n-000255d0: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n-000255e0: 2e20 2028 6c69 6e65 2020 3135 290a 2a20 . (line 15).* \n-000255f0: 7472 616e 736c 6174 696f 6e20 7472 616e translation tran\n-00025600: 7366 6f72 6d20 3c32 3e3a 2020 2020 2020 sform <2>: \n-00025610: 2020 2020 2020 2041 2068 6965 7261 7263 A hierarc\n-00025620: 6869 6361 6c20 6d6f 6465 6c2e 0a20 2020 hical model.. \n+000254f0: 2054 7261 6e73 666f 726d 206c 6974 6572 Transform liter\n+00025500: 616c 732e 2020 286c 696e 6520 2032 3529 als. (line 25)\n+00025510: 0a2a 2074 7261 6e73 666f 726d 2c20 7669 .* transform, vi\n+00025520: 6577 203c 313e 3a20 2020 2020 2020 2020 ew <1>: \n+00025530: 2020 2020 2020 2020 2020 5472 616e 7366 Transf\n+00025540: 6f72 6d20 6c69 7465 7261 6c73 2e20 2028 orm literals. (\n+00025550: 6c69 6e65 2020 3335 290a 2a20 7472 616e line 35).* tran\n+00025560: 736c 6174 696f 6e20 7472 616e 7366 6f72 slation transfor\n+00025570: 6d3a 2020 2020 2020 2020 2020 2020 2020 m: \n+00025580: 2020 204f 626a 6563 7420 7472 616e 7366 Object transf\n+00025590: 6f72 6d73 2e20 2020 286c 696e 6520 2034 orms. (line 4\n+000255a0: 3729 0a2a 2074 7261 6e73 6c61 7469 6f6e 7).* translation\n+000255b0: 2074 7261 6e73 666f 726d 203c 313e 3a20 transform <1>: \n+000255c0: 2020 2020 2020 2020 2020 2020 5472 616e Tran\n+000255d0: 7366 6f72 6d20 6c69 7465 7261 6c73 2e20 sform literals. \n+000255e0: 2028 6c69 6e65 2020 3135 290a 2a20 7472 (line 15).* tr\n+000255f0: 616e 736c 6174 696f 6e20 7472 616e 7366 anslation transf\n+00025600: 6f72 6d20 3c32 3e3a 2020 2020 2020 2020 orm <2>: \n+00025610: 2020 2020 2041 2068 6965 7261 7263 6869 A hierarchi\n+00025620: 6361 6c20 6d6f 6465 6c2e 0a20 2020 2020 cal model.. \n 00025630: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025640: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025650: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025660: 2020 2020 2020 2020 2020 2028 6c69 6e65 (line\n-00025670: 2020 3437 290a 2a20 7472 616e 7370 6172 47).* transpar\n-00025680: 656e 6379 3a20 2020 2020 2020 2020 2020 ency: \n-00025690: 2020 2020 2020 2020 2020 2020 2020 2054 T\n-000256a0: 7261 6e73 7061 7265 6e63 792e 2020 2020 ransparency. \n-000256b0: 2020 2020 286c 696e 6520 2020 3629 0a2a (line 6).*\n-000256c0: 2074 776f 2d6f 7065 7261 6e64 2066 6f72 two-operand for\n-000256d0: 6d3a 2020 2020 2020 2020 2020 2020 2020 m: \n-000256e0: 2020 2020 2020 2020 5477 6f2d 6f70 6572 Two-oper\n-000256f0: 616e 6420 2862 696e 6172 7929 2066 6f72 and (binary) for\n-00025700: 6d73 2e0a 2020 2020 2020 2020 2020 2020 ms.. \n+00025660: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00025670: 3437 290a 2a20 7472 616e 7370 6172 656e 47).* transparen\n+00025680: 6379 3a20 2020 2020 2020 2020 2020 2020 cy: \n+00025690: 2020 2020 2020 2020 2020 2020 2054 7261 Tra\n+000256a0: 6e73 7061 7265 6e63 792e 2020 2020 2020 nsparency. \n+000256b0: 2020 286c 696e 6520 2020 3629 0a2a 2074 (line 6).* t\n+000256c0: 776f 2d6f 7065 7261 6e64 2066 6f72 6d3a wo-operand form:\n+000256d0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000256e0: 2020 2020 2020 5477 6f2d 6f70 6572 616e Two-operan\n+000256f0: 6420 2862 696e 6172 7929 2066 6f72 6d73 d (binary) forms\n+00025700: 2e0a 2020 2020 2020 2020 2020 2020 2020 .. \n 00025710: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025720: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025730: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025740: 2020 286c 696e 6520 2020 3629 0a2a 2075 (line 6).* u\n-00025750: 6e61 7279 2066 6f72 6d3a 2020 2020 2020 nary form: \n+00025740: 286c 696e 6520 2020 3629 0a2a 2075 6e61 (line 6).* una\n+00025750: 7279 2066 6f72 6d3a 2020 2020 2020 2020 ry form: \n 00025760: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025770: 2020 2020 2020 556e 6172 7920 666f 726d Unary form\n-00025780: 732e 2020 2020 2020 2020 2028 6c69 6e65 s. (line\n-00025790: 2020 2036 290a 2a20 7665 6374 6f72 3a20 6).* vector: \n+00025770: 2020 2020 556e 6172 7920 666f 726d 732e Unary forms.\n+00025780: 2020 2020 2020 2020 2028 6c69 6e65 2020 (line \n+00025790: 2036 290a 2a20 7665 6374 6f72 3a20 2020 6).* vector: \n 000257a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000257b0: 2020 2020 2020 2020 2020 2020 2020 204f O\n-000257c0: 626a 6563 7420 7472 616e 7366 6f72 6d73 bject transforms\n-000257d0: 2e20 2020 286c 696e 6520 2034 3829 0a2a . (line 48).*\n-000257e0: 2076 6563 746f 7220 6465 6669 6e69 7469 vector definiti\n-000257f0: 6f6e 3a20 2020 2020 2020 2020 2020 2020 on: \n-00025800: 2020 2020 2020 2020 506f 6c79 6c69 6e65 Polyline\n-00025810: 2073 7765 6570 732e 2020 2020 2028 6c69 sweeps. (li\n-00025820: 6e65 2020 3139 290a 2a20 7665 6374 6f72 ne 19).* vector\n-00025830: 206c 6974 6572 616c 3a20 2020 2020 2020 literal: \n-00025840: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025850: 2050 6f69 6e74 2061 6e64 2076 6563 746f Point and vecto\n-00025860: 7220 6c69 7465 7261 6c73 2e0a 2020 2020 r literals.. \n+000257b0: 2020 2020 2020 2020 2020 2020 204f 626a Obj\n+000257c0: 6563 7420 7472 616e 7366 6f72 6d73 2e20 ect transforms. \n+000257d0: 2020 286c 696e 6520 2034 3829 0a2a 2076 (line 48).* v\n+000257e0: 6563 746f 7220 6465 6669 6e69 7469 6f6e ector definition\n+000257f0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n+00025800: 2020 2020 2020 506f 6c79 6c69 6e65 2073 Polyline s\n+00025810: 7765 6570 732e 2020 2020 2028 6c69 6e65 weeps. (line\n+00025820: 2020 3139 290a 2a20 7665 6374 6f72 206c 19).* vector l\n+00025830: 6974 6572 616c 3a20 2020 2020 2020 2020 iteral: \n+00025840: 2020 2020 2020 2020 2020 2020 2020 2050 P\n+00025850: 6f69 6e74 2061 6e64 2076 6563 746f 7220 oint and vector \n+00025860: 6c69 7465 7261 6c73 2e0a 2020 2020 2020 literals.. \n 00025870: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025880: 2020 2020 2020 2020 2020 2020 2020 2020 \n 00025890: 2020 2020 2020 2020 2020 2020 2020 2020 \n-000258a0: 2020 2020 2020 2020 2020 286c 696e 6520 (line \n-000258b0: 2020 3629 0a2a 2076 6563 746f 7220 7265 6).* vector re\n-000258c0: 6665 7265 6e63 653a 2020 2020 2020 2020 ference: \n-000258d0: 2020 2020 2020 2020 2020 2020 2020 466f Fo\n-000258e0: 726d 7320 6f66 2072 6566 6572 656e 6365 rms of reference\n-000258f0: 732e 2028 6c69 6e65 2020 3135 290a 2a20 s. (line 15).* \n-00025900: 7669 6577 2074 7261 6e73 666f 726d 3a20 view transform: \n+000258a0: 2020 2020 2020 2020 286c 696e 6520 2020 (line \n+000258b0: 3629 0a2a 2076 6563 746f 7220 7265 6665 6).* vector refe\n+000258c0: 7265 6e63 653a 2020 2020 2020 2020 2020 rence: \n+000258d0: 2020 2020 2020 2020 2020 2020 466f 726d Form\n+000258e0: 7320 6f66 2072 6566 6572 656e 6365 732e s of references.\n+000258f0: 2028 6c69 6e65 2020 3135 290a 2a20 7669 (line 15).* vi\n+00025900: 6577 2074 7261 6e73 666f 726d 3a20 2020 ew transform: \n 00025910: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025920: 2020 2020 2020 2054 7261 6e73 666f 726d Transform\n-00025930: 206c 6974 6572 616c 732e 2020 286c 696e literals. (lin\n-00025940: 6520 2032 3529 0a2a 2076 6965 7720 7472 e 25).* view tr\n-00025950: 616e 7366 6f72 6d20 3c31 3e3a 2020 2020 ansform <1>: \n-00025960: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025970: 5472 616e 7366 6f72 6d20 6c69 7465 7261 Transform litera\n-00025980: 6c73 2e20 2028 6c69 6e65 2020 3335 290a ls. (line 35).\n-00025990: 2a20 7669 7274 7561 6c20 6361 6d65 7261 * virtual camera\n-000259a0: 3a20 2020 2020 2020 2020 2020 2020 2020 : \n-000259b0: 2020 2020 2020 2020 204f 7665 7276 6965 Overvie\n-000259c0: 772e 2020 2020 2020 2020 2020 2020 286c w. (l\n-000259d0: 696e 6520 2038 3129 0a2a 2077 6869 7465 ine 81).* white\n-000259e0: 2073 7061 6365 3a20 2020 2020 2020 2020 space: \n+00025920: 2020 2020 2054 7261 6e73 666f 726d 206c Transform l\n+00025930: 6974 6572 616c 732e 2020 286c 696e 6520 iterals. (line \n+00025940: 2032 3529 0a2a 2076 6965 7720 7472 616e 25).* view tran\n+00025950: 7366 6f72 6d20 3c31 3e3a 2020 2020 2020 sform <1>: \n+00025960: 2020 2020 2020 2020 2020 2020 2020 5472 Tr\n+00025970: 616e 7366 6f72 6d20 6c69 7465 7261 6c73 ansform literals\n+00025980: 2e20 2028 6c69 6e65 2020 3335 290a 2a20 . (line 35).* \n+00025990: 7669 7274 7561 6c20 6361 6d65 7261 3a20 virtual camera: \n+000259a0: 2020 2020 2020 2020 2020 2020 2020 2020 \n+000259b0: 2020 2020 2020 204f 7665 7276 6965 772e Overview.\n+000259c0: 2020 2020 2020 2020 2020 2020 286c 696e (lin\n+000259d0: 6520 2038 3129 0a2a 2077 6869 7465 2073 e 81).* white s\n+000259e0: 7061 6365 3a20 2020 2020 2020 2020 2020 pace: \n 000259f0: 2020 2020 2020 2020 2020 2020 2020 2020 \n-00025a00: 2020 4472 6177 696e 6720 6120 736f 6c69 Drawing a soli\n-00025a10: 642e 2020 2020 2028 6c69 6e65 2020 3235 d. (line 25\n-00025a20: 290a 2a20 7768 6974 6520 7370 6163 6520 ).* white space \n-00025a30: 3c31 3e3a 2020 2020 2020 2020 2020 2020 <1>: \n-00025a40: 2020 2020 2020 2020 2020 2044 7261 7769 Drawi\n-00025a50: 6e67 2061 2073 6f6c 6964 2e20 2020 2020 ng a solid. \n-00025a60: 286c 696e 6520 2032 3929 0a2a 2077 6869 (line 29).* whi\n-00025a70: 7465 2073 7061 6365 203c 323e 3a20 2020 te space <2>: \n+00025a00: 4472 6177 696e 6720 6120 736f 6c69 642e Drawing a solid.\n+00025a10: 2020 2020 2028 6c69 6e65 2020 3235 290a (line 25).\n+00025a20: 2a20 7768 6974 6520 7370 6163 6520 3c31 * white space <1\n+00025a30: 3e3a 2020 2020 2020 2020 2020 2020 2020 >: \n+00025a40: 2020 2020 2020 2020 2044 7261 7769 6e67 Drawing\n+00025a50: 2061 2073 6f6c 6964 2e20 2020 2020 286c a solid. 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-347,15 +347,15 @@\n reference to special arg %d cannot accept a point\n reference to special arg %d cannot accept a vector\n reference to special arg %d: out of range [1-%d]\n bad tick option character in #%d'%c (try #{%d}'%c)\n unknown special arg from flatten\n use of '#' not as special arg (try ##)\n can't open document template '%s%' for input\n-%% Sketch output, version 0.3 (build 7d, Fri Jun 20 19:43:13 2025)\n+%% Sketch output, version 0.3 (build 7d, Sun May 19 15:36:52 2024)\n %% Output language: %s\n document template with no escape '%s' has been ignored\n more than one escape in document template; all but first ignored\n operands of + (types %s and %s) cannot be added\n operands of - (types %s and %s) cannot be subtracted\n operands of * (types %s and %s) cannot be multiplied\n operands of 'then' (types %s and %s) cannot be multiplied\n"}, {"source1": "readelf --wide --decompress --hex-dump=.rodata {}", "source2": "readelf --wide --decompress --hex-dump=.rodata {}", 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./usr/lib/debug/\n drwxr-xr-x 0 root (0) root (0) 0 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/\n-drwxr-xr-x 0 root (0) root (0) 0 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/18/\n--rw-r--r-- 0 root (0) root (0) 218560 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/18/d71aec6ad7e2bb10f3dabb8c0d08ac1ce88ae0.debug\n+drwxr-xr-x 0 root (0) root (0) 0 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/f4/\n+-rw-r--r-- 0 root (0) root (0) 218560 2020-11-07 02:36:18.000000 ./usr/lib/debug/.build-id/f4/92111ee969ae3afc2f6a0acab7afdcb69492da.debug\n drwxr-xr-x 0 root (0) root (0) 0 2020-11-07 02:36:18.000000 ./usr/share/\n drwxr-xr-x 0 root (0) root (0) 0 2020-11-07 02:36:18.000000 ./usr/share/doc/\n lrwxrwxrwx 0 root (0) root (0) 0 2020-11-07 02:36:18.000000 ./usr/share/doc/sketch-dbgsym -> sketch\n"}, {"source1": "./usr/lib/debug/.build-id/18/d71aec6ad7e2bb10f3dabb8c0d08ac1ce88ae0.debug", "source2": 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Owner Data size \tDescription\n GNU 0x00000010\tNT_GNU_ABI_TAG (ABI version tag)\t OS: Linux, ABI: 3.2.0\n"}]}]}, {"source1": "xz --list", "source2": "xz --list", "unified_diff": "@@ -1,13 +1,13 @@\n Streams: 1\n Blocks: 1\n- Compressed size: 191.4 KiB (196020 B)\n+ Compressed size: 191.4 KiB (196028 B)\n Uncompressed size: 220.0 KiB (225280 B)\n Ratio: 0.870\n Check: CRC64\n Stream Padding: 0 B\n Streams:\n Stream Blocks CompOffset UncompOffset CompSize UncompSize Ratio Check Padding\n- 1 1 0 0 196020 225280 0.870 CRC64 0\n+ 1 1 0 0 196028 225280 0.870 CRC64 0\n Blocks:\n Stream Block CompOffset UncompOffset TotalSize UncompSize Ratio Check\n- 1 1 12 0 195984 225280 0.870 CRC64\n+ 1 1 12 0 195992 225280 0.870 CRC64\n"}]}]}]}